Chopper 2004
No, because the Apache crews would not be able to attend the briefing at Nellis AFB as by the time they got to the 'play area' to the North of Dreamland, everyone else would be going home! They would probably need a FARP (Forward Air Refuelling Point) set out in the desert and they would never make it back to the debrief on time.
Just think about the physics of the situation. It used to take 20-40 minutes to get back to Nellis AFB from the 'play area' at ~420kts ground speed - for an Apache going at ~120kts it would take 1hr-2hrs!!! Even the poor old SF C-130s would struggle to make the timings at around 210kts ground speed.
So in my experience, to play on Ex RED FLAG as a participant, it would not really be possible. We used to get the odd HIND flown by the REDs (Agressors) in the training scenarios, but never seen an Allied RW participant on the BLUE side. Also, the cost would also likely be prohibitive.
iRaven