Upload avatar image from the checkout using the PMPro Register Helper Add On. No other plugins required.

pmpro-file-upload-avatar-register-helper.php

/*
 * Add WP User Avatar from Register Helper field during checkout.
 */
function my_updated_user_meta($meta_id, $user_id, $meta_key, $meta_value) {
  // Change user_avatar to your Register Helper file upload name.
  if( 'user_avatar' == $meta_key) {
    $filename = $meta_value['fullpath'];
    $filetype = wp_check_filetype( basename( $filename ), null );
    $wp_upload_dir = wp_upload_dir();
    $attachment = array(
    	'post_mime_type' => $filetype['type'],
    	'post_title'     => preg_replace( '/\.[^.]+$/', '', wp_upload_dir().$filename ),
    	'post_status'    => 'inherit'
    );
    $attach_id = wp_insert_attachment( $attachment, $filename);
    // Make sure that this file is included, as wp_generate_attachment_metadata() depends on it.
    require_once( ABSPATH . 'wp-admin/includes/image.php' );
    $attach_data = wp_generate_attachment_metadata( $attach_id, $filename );
    wp_update_attachment_metadata( $attach_id, $attach_data );
    update_user_meta($user_id, 'wp_user_avatar', $attach_id);    
  }
}
add_action('added_user_meta', 'my_updated_user_meta', 10, 4);
add_action('updated_user_meta', 'my_updated_user_meta', 10, 4);

function my_user_avatar_filter( $avatar, $id_or_email, $size, $default, $alt ) {
    $my_user = get_userdata( $id_or_email );
    if( !empty( $my_user ) ){
        $avatar_id = get_user_meta( $my_user->ID, 'wp_user_avatar', true );
        if( !empty( $avatar_id ) ) {
            $avatar = wp_get_attachment_url( $avatar_id, $size );
            $avatar = "<img alt='{$alt}' src='{$avatar}' class='avatar avatar-{$size} photo' height='{$size}' width='{$size}' />";
        }
    }
    return $avatar;
}
add_filter( 'get_avatar', 'my_user_avatar_filter', 20, 5 );

function my_pmprorh_init_2()
{
    //don't break if Register Helper is not loaded
    if(!function_exists("pmprorh_add_registration_field"))
    {
        return false;
    }
    //define the fields
    $fields = array();
    $fields[] = new PMProRH_Field(
        "user_avatar",              // input name, will also be used as meta key
        "file",                 // type of field
        array(
            "label"=>"Avatar",
            "hint"=>"Recommended size is 100px X 100px",
            "profile"=>true,    // show in user profile
        ));

    //add the fields into a new checkout_boxes are of the checkout page
    foreach($fields as $field)
        pmprorh_add_registration_field(
            "checkout_boxes", // location on checkout page
            $field            // PMProRH_Field object
        );
    //that's it. see the PMPro Register Helper readme for more information and examples.
}
add_action("init", "my_pmprorh_init_2");