Never actually tried it, but this describes the method I would think would work. It depends on it NOT being in Standby mode (i.e. if you can connect to the recipient right now with read access, you'll need to fiddle with it to change it to Norecovery mode)
This is also assuming that "move" means move to another drive/directory on the same server. If you're talking another server, then No.
But to be honest, I would use this an exercise to test and update those documents that describe how to rebuild the standby server and re-restore from a full backup.
EDIT BASED ON YOUR EDIT : Yes, you could stop SQL, copy the MDF and LDF to another server and attach them, restart SQL and log shipping should not be affected
But if you have an on-going need to do this, you could change the log shipping to set the database to standby, which would allow you to do your analysis queries against the active log-shipping recipient database, as long as they are read-only queries, and you deal with the fact that log-shipping will be suspended while you are connected to the database.