Can burning incense in the same space with a computer harm a central
processing unit?

My guess is significant harm is very unlikely.   Neil

Be careful about ash, though. Smoking and incense both have
particulates that are pulled through fans.

Your processor should be fine, as the fan that's mounted on your
processor is just drawing air over the heatsink, not into/over/thru
the processors itself. Unless the incense is very hot and is
interfering with the proper cooling of the computer then you should
have no problem.