Restore MacBook Pro backup to a Mac Mini? I've got to drop my MBP (2010 model) in to the Apple store asap to get it repaired and it'll be out of action for a week during a time I need it most. My thought process is, due to the urgency of it all, to get a Mac Mini to tide me over until the repair is complete and keep working in the mean time.

If I buy a Mac Mini, could I just do a time machine restore of my MBP to that and be up and running? Are there any associated problems?

Second thought is also, could I just swap out the drive in the Mac Mini with that of my MBP and be up and running without issue? (I know I'll have to put my MBP in for repair with a drive in, got that thought covered).
I've had the best results restoring from Time Machine to a freshly formatted drive. I did this for a machine with lots of system modifications, (httpd.conf, ssh_config) and all of these files were restored. When I did that with an OS in place these files were missed. There were no problems when I restored to a clean drive. Everything was restored properly. So, if you buy a Mac Mini, format the drive before running the Time Machine restore.

I recommend sending machines to Apple as stock as possible. I've put in known bad hard drives with the Apple Logo on them when sending a machine back to Apple. The hard drive was replaced and the primary problem was fixed. The drive swap would be fine, but unless you are in a big hurry I'd discourage it.