Most repair shops would likely only charge you a very minimal fee if you took the power supply to them for testing, which is a far better idea than taking a chance with the rest of your hardware.
Take a look at your carpet where the unit was sitting, and see if any of the fibers are burnt, smell burnt or look melted. If they are, the smell was likely from the carpet and not the rig itself. I'd be very cautious whichever way you decide to go and I think it would still be a good idea to remove the unit and test it, or have it tested, before continuing use with it installed in the system.
If airflow through the PSU was blocked, it's far, far more likely that damage or unusual burnt smells would come from the PSU than they would from the motherboard. In order for the motherboard to be damaged by the PSU overheating, the PSU would have to have already been damaged beyond the point where it was still safe for use. If there is any damage to the motherboard, the PSU is already shot.
Sitting computers on carpeted floors without a base of some kind to keep the unit above the carpet itself is a common enough fail on the part of the unwary user, and usually results in an overheated PSU or burnt carpet, not a damaged motherboard, unless you continue to use it after the damage has occurred.