MultiSQLConnection.ps1

#Driver variables, will become params
$MaxConnections = 50
$Server= 'localhost'

#Set Initial collections and objects    
$SqlInstance = New-Object Microsoft.SqlServer.Management.Smo.Server $Server
$DbConnections = @();
$dbs = $SqlInstance.Databases | Where-Object {$_.IsSystemObject -eq 0} 

#Build DB connection array
for($i=0;$i -le $MaxConnections;$i++){
  $randdb = Get-Random -Minimum 1 -Maximum $dbs.Count
  $DbConnections += $dbs[$randdb].Name
}

#Loop through DB Connection array, create script block for establishing SMO connection/query
#Start-Job for each script block
foreach ($DBName in $DbConnections ) {
$cmdstr =@"
`[System.Reflection.Assembly]::LoadWithPartialName("Microsoft.SqlServer.Smo")
`$SqlConn = New-Object Microsoft.SqlServer.Management.Smo.Server $Server
`$SqlConn.Databases['$DBName'].ExecuteNonQuery("WAITFOR DELAY '00:05:00'")
"@
$cmd = [ScriptBlock]::Create($cmdstr)
Start-Job -ScriptBlock $cmd
}

I kept all this in the SMO for simplicity. It takes a couple to fire up all the connections and there's probably some refinement that can happen there, but this will get a simple batch of connections open. For the database connections, I randomized what databases are connected to by building an initial collection of database names. I ignore system databases (note, this will blow up if you only have 1 user database). Be aware of the escape characters in the scriptblock building section.