I presume compression shorts are more-or-less what they sound like, in which case they should be fine.

My experience:
- Boxers: a world of pain and unexpected danger. A delight to change into at the end of the ride.
- Cotton briefs/bikini undies: OK for a block but quickly get sweaty and then chafe as if ground glass was glued to the seams.
- Lycra short trunks: Breathe really well, but ride up. Not as good as I'd hoped.
- Coolmax short trunks: Not bad.
- Nylon mesh short trunks: Not great. Not enough flexibility/softness in the weave.
- Coolmax/coolmax mesh long trunks: THE BEST for wearing under normal clothes. The ones I have don't ride up too much, breathe well, dry fast and don't have seams where they hurt.
- Bike shorts underneath: OK while riding but you need to change out of them, they stay wet forever.