Sounds ignition related to me. You need to run that check engine light and see what codes come up; the intercooler pump does not cause a CEL. Plus, you mentioned restarting the car fixes the problem, which also sounds ignition related. The intercooler pump will never cause the revs to "drop". It will cause a power loss that makes the engine almost impossible to hit high revs, but the revs will not drop during mid-acceleration. Finally, you mentioned this happens before the car warms up. The intercooler pump doesn't usually cause issues until the engine supercharges absorbs and creates some heat.

The other likelyhood is the temp sensor that someone mentioned already. If this is reporting an inaccurate temp, the engine could be turning off the S/C, but you revs still shouldn't "drop" the way you mentioned.

Good Luck!