Restore MacBook Pro backup to a Mac Mini?
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.