If all you need to do is run Outlook as that user, I think TheCleaner's suggestion is probably the best option. You can do this from the command line, and then change the user that the service runs as from the services console. Check out the link below if you would like to do it without a third party app.
https://stackoverflow.com/questions/3582108/create-windows-service-from-executable
In response to comments, here is a starter for how to start with powershell. If this needs adjustment, please provide more context.
$hostname = "serverName"
$username = "CKnutson"
$processName = "outlook"
$session = New-PSSession $hostname
Enter-PSSession $session
$processes = @()
$processes += Get-Process -IncludeUserName | Where-Object {$_.UserName -like "*$username" -and $_.Name -like "$processName"}
if ($processes.Count -eq 0) {
Start-Process -FilePath "C:\proc.exe" -ArgumentList "-Silent" -LoadUserProfile
}
That should open a remote console to the server that you want to run outlook, check if there is a running process for that user, and then start it if needed.