Logon on a user and gpedit.msc

1. I assume one can call a powershell script from the logon/logoff script
section of group policy (gpedit.msc, under user configuration, windows
settings, scripts logon/logonoff). Is that right?

2. I want to use a script to login a user. The script would run whenever a
(remote) user logoffs (I'm attaching it to gpedit policy on logoff scripts).

Can this be done, and is there sample code? I just need script to detect if
there is a shutdown going on, and if not, to login a user (technically, the
same user being logged off).

a: A remote desktop user logoffs.
b: The logoff script entered in gpedit.msc runs.
c: That script logs on a local user, as long as we're not in a shutdown (as
long as logoff in (a) wasn't part of a shutdown).

Thanks.