The answer seems to be NO. Someone claims to have read documentation stating that they cannot be combined. However......
People claim to have gotten both. I speculate that what is happening in those cases is that the dealer is selling the vehicle at a price equal to the supplier pricing and simply not calling it supplier pricing. I think the dealer simply loses whatever they get back from GM for selling at supplier pricing. The supplier pricing is somewhere near invoice so they are still making the holdback and whatever other dealer incentives that are in place that we don't know about. Either that or the dealer is doing both and hoping that they do not get caught in an audit by GM
I was one of those people that was told by my initial dealer/salesperson that they would be able to combine the Conquest with the Supplier discount. However, when my vehicle actually arrived, the story changed and they weren't able to do both.
I also called the general GM phone number to ask, and they confirmed that these two offers are not able to be combined - it's one or the other.
Any dealer that is doing this, isn't doing it correctly and will get dinged by GM once they process the purchase. Of course if you can get a dealer to do it before they know better, more power to you!
I was the one that witnessed documentation that they can NOT do both. However, I was also told initially that they could, so what they ended up doing is not giving me supplier price, but matched it, and gave me the Conquest Rebate. So in short, no they cannot do both to my knowledge and experience.
I asked for part of the kickback they get from GM for selling at supplier and he knocked another $300 off our Enclave. I felt good about it because it was their first one and he didn't even have to sell it at supplier.