Good questions. But if the relays on the RCM have dirty or pitted contacts, then I believe it can affect the voltage going through...to the ECM, TCM, fuel pump, and the air pump. As everyone says, the Crossfire's electronics are very sensitive about voltage.
I hate throwing parts at a problem....but tighed1 can repair the RCM and replace relays...or you could buy a spare on amazon. This is the one I bought for my 2005 Crossfire roadster.
I wasn't having the no-start issue, but I bought a new RCM, plugged it in, and I swear, the car ran better. I then, sent off my old RCM to tighed1 for his magic work. I've got a spare RCM, now.