What do you know, it worked! Here's my modified code, in case people would like to see.
$UserList = Get-CASMailbox -Filter {hasactivesyncdevicepartnership -eq $true -and -not displayname -like "CAS_{*"} | Get-Mailbox $UserList | ForEach-Object { get-mailbox $_.alias | Select-Object -Property Name | Out-File -Append d:\mobiles.txt Get-MobileDeviceStatistics -Mailbox $_.alias | ft -Property DevicePhoneNumber, DeviceModel, DeviceOS, FirstSyncTime -AutoSize | out-file -Append d:\mobiles.txt }