I don't think that's true. The Khomeini clan do rely on IRGC to remain in power somewhat, but it also has strong influence towards the civilian government, and the OPA it ran on the Mullah at the start of the war, getting a non-mullah elected supreme leader at a very cheap price prove they rely on more than their central militia. A lot of the clans who supported the Shah during the original coup also seems to support the regime, which makes the north stable. The western part of the country, despite insurgents/independence groups, seems to have reported their hatred of S.Hussein towards the US (to be fair, the chemical weapons Hussein used to bomb their village were from the US), which means they might choose to fight the US rather than the regime.

Imho the regime was made stronger because of this war. It was really a bad moment to strike. Khomeini had a cancer, and waiting for his death and the succession crisis that would have ensued would have been a better choice. Now the regime is stronger than ever.

Although my real thoughts is that this strength the Khomeini project is temporary, in the sense that the only reason the regime lasted this long before was because the power was shared. If they keep pushing for more control, without sharing, they will end up loosing everything.