This script makes a change to an account and then checks to see how long it takes before that change is replicated on Office365. The script takes advantage of ParameterNames to make it easy to either pass in a credential object or string user/pass variables. I have also added a switch for ExchangeOnline, the original author used the get-mailbox …

Get-SyncDelay.ps1

<#
	.SYNOPSIS
		Get the amount of time for an update to Office365
	.DESCRIPTION
		This script makes a change to an account and then checks to see how long
		it takes before that change is replicated on Office365.
	.PARAMETER Tenant
		This is your tenant name
	.PARAMETER Account
		This is the test account name
	.PARAMETER Credential
		This is a tenant account with rights to modify user objects
	.EXAMPLE
		.\Get-SyncDelay.ps1 -UserName tenantadmin@myTenant.onmicrosoft.com -Password mYP@ssw0rd -Tenant myTenant.onmicrosoft.com -Account tstAcct01

		Get-LogFile -LogName Office365-Sync-Check |Where-Object -Property EventID -eq 0

		EventRecord : 00000003
		LogName     : Office365-Sync-Check
		Source      : Set-MsolUser
		Time        : 03/03/2015 17:39:42
		EventID     : 0
		EntryType   : Information
		Message     : Total Sync Delay in Seconds 0
	
		Description
		-----------
		This example shows using the script by passing in a valid admin account and password
		as strings, useful for certain types of automation. The Get-LogFile cmdlet from LogFiles
		was used to get the delay.
	.EXAMPLE
		$Credential = New-Object System.Management.Automation.PSCredential ('tenantadmin@myTenant.onmicrosoft.com', (ConvertTo-SecureString -String 'mYP@ssw0rd' -AsPlainText -Force));
		.\Get-SyncDelay.ps1 -Credential $Credential -Tenant myTenant.onmicrosoft.com -Account tstAcct01

		Starting Sync Check
		Change DisplayName property of tstAcct01@myTenant.onmicrosoft.com to Delay Monitor 1425404038


		Days              : 0
		Hours             : 0
		Minutes           : 0
		Seconds           : 1
		Milliseconds      : 78
		Ticks             : 10781009
		TotalDays         : 1.24780196759259E-05
		TotalHours        : 0.000299472472222222
		TotalMinutes      : 0.0179683483333333
		TotalSeconds      : 1.0781009
		TotalMilliseconds : 1078.1009
	
		Description
		-----------
		This example shows passing in a credential object which is useful for running the
		script manually.
	.NOTES
		This came from code that was provided to me originally through the
		Office365 HiEd mailling list. 

		Many thanks to Jacob Fortune for sharing!

		In order for this script to work you will need the MSONline Module
		that you can download from the first link. You will also need my
		LogFiles module that you can download from the second link. If you would
		rather write to the Windows EventLog, you can easily make that modification
		yourself, just remember to remove the Import-Module Logfiles statement
		in the Begin section.
	.LINK
		https://msdn.microsoft.com/en-us/library/azure/jj151815.aspx
	.LINK
		https://raw.githubusercontent.com/jeffpatton1971/mod-posh/master/powershell/production/includes/LogFiles.psm1
#>
Param
(
	[Parameter(Mandatory=$true,ParameterSetName='Credential')]
	[System.Management.Automation.PSCredential]$Credential,
	[Parameter(Mandatory=$true,ParameterSetName='NoCredential')]
	[string]$UserName,
	[Parameter(Mandatory=$true,ParameterSetName='NoCredential')]
	[string]$Password,
	[Parameter(Mandatory=$true)]
	[string]$Tenant,
	[Parameter(Mandatory=$true)]
	[string]$Account,
	[Parameter(Mandatory=$false)]
	[switch]$ExchangeOnline
)
Begin
{
	#
	# Import the MSONLINE module
	# Import the LogFiles module
	#
	$LogName = "Office365-Sync-Check";
	try
	{
		Import-Module MSOnline;
		
		if ($PSCmdlet.ParameterSetName -eq 'NoCredential')
		{
			$Credential = New-Object System.Management.Automation.PSCredential ($UserName, (ConvertTo-SecureString -String $Password -AsPlainText -Force));
			Import-Module C:\projects\mod-posh\PowerShell\Production\Includes\LogFiles.psm1;
			}

		if ($ExchangeOnline)
		{
			#
			# EOP Standalone URL 
			# $EoURI = "https://ps.protection.outlook.com/powershell-liveid"
			#
			# Exchange Online Tenant
			$EoUri = "https://outlook.office365.com/powershell-liveid"
			$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri $EoUri -Credential $Credential -Authentication Basic -AllowRedirection;
			#
			# Import ExchangeOnlline Cmdlets
			#
			Import-PSSession $Session;
			}		
		Connect-MsolService -Credential $Credential;
		}
	catch
	{		
		$LogMessage = $Error[0].Exception;
		if ($PSCmdlet.ParameterSetName -eq 'Credential')
		{
			Write-Error $LogMessage;
			}
		else
		{
			Write-LogFile -LogName $LogName -Source "Script Init" -EventId 1 -EntryType "Error" -Message $LogMessage;
			}
		break;
		}
	}
Process
{
	try
	{
		if ($PSCmdlet.ParameterSetName -eq 'Credential')
		{
			Write-Host "Starting Sync Check";
			}
		else
		{
			Write-LogFile -LogName $LogName -Source "Begin Sync Check" -EventId 10 -EntryType "Information" -Message "Starting Sync Check";
			}
		$TimeStamp = "{0:G}" -f [int][double]::Parse((Get-Date -UFormat %s));
		$UserPrincipalName = "$($Account)@$($Tenant)";
		$DisplayName = "Delay Monitor $($TimeStamp)";
		
		$StartTime = Get-Date;
		Set-MsolUser -UserPrincipalName $UserPrincipalName -DisplayName $DisplayName;
		
		if ($PSCmdlet.ParameterSetName -eq 'Credential')
		{
			Write-Host "Change DisplayName property of $($UserPrincipalName) to $($DisplayName)";
			}
		else
		{
			Write-LogFile -LogName $LogName -Source "Set-MsolUser" -EventId 10 -EntryType "Information" -Message "Change DisplayName property of $($UserPrincipalName) to $($DisplayName)";
			}

		if ($ExchangeOnline)
		{
			$MsolUser = Get-Mailbox -Identity $UserPrincipalName |Select-Object -Property DisplayName, WhenChanged; 
			}
		else
		{
			$MsolUser = Get-MsolUser -UserPrincipalName $UserPrincipalName |Select-Object -Property DisplayName, WhenChanged;
			}
		while ($MsolUser.DisplayName -ne $DisplayName)
		{	
			if ($PSCmdlet.ParameterSetName -eq 'Credential')
			{
				Write-Host "Getting DisplayName property of $($UserPrincipalName)";
				}
			else
			{
				Write-LogFile -LogName $LogName -Source "Get-MsolUser" -EventId 10 -EntryType "Information" -Message "Getting DisplayName property of $($UserPrincipalName)";
				}
			Start-Sleep -Seconds 5;
			if ($ExchangeOnline)
			{
				$MsolUser = Get-Mailbox -Identity $UserPrincipalName |Select-Object -Property DisplayName, WhenChanged; 
				}
			else
			{
				$MsolUser = Get-MsolUser -UserPrincipalName $UserPrincipalName |Select-Object -Property DisplayName, WhenChanged;
				}
			}
		
		$EndTime = Get-Date;
		$Delay = New-TimeSpan -Start $StartTime -End $EndTime

		if ($PSCmdlet.ParameterSetName -eq 'Credential')
		{
			return $Delay;
			}
		else
		{
			Write-LogFile -LogName $LogName -Source "Set-MsolUser" -EventId 0 -EntryType "Information" -Message "Total Sync Delay in Seconds $($Delay.Seconds)";
			}
		}
	catch
	{
		$LogMessage = $Error[0].Exception;
		if ($PSCmdlet.ParameterSetName -eq 'Credential')
		{
			Write-Error $LogMessage;
			}
		else
		{
			Write-LogFile -LogName $LogName -Source "Script Process" -EventId 1 -EntryType "Error" -Message $LogMessage;
			}
		break;
		}
	}
End
{
	}

Updated this with a switch for ExchangeOnline as well as the code needed to pull in the EOP powershell cmdlets