Your mix and match question is quite a tough one, and I have no idea what the answer is since I don't run any sram drivetrain. However I can offer some suggestions that hopefully might help you work out the answer yourself.
Firstly if we are talking about mix and match for a triple, indexing will be super tricky and all bets are off. But since you are running a Red I presume we are talking about a double.
For shifting a double, the fundamental piece of the jigsaw in this case is that the 7800 is a Shimano road front mech and it requires just under 7mm of cable pull from the shifter for a perfect shift.
The second piece of the jigsaw is that for doubles it should work as long as the shifter pulls either the right amount of cable or more. Too little is no good for the obvious reason. Too much should still be ok because the shift from the small onto the large ring can be made to work simply by allowing the cable to be loose when at the small ring (correct indexing will be set by the limit screw, not cable tension), and the mech's return spring will take care of the reverse shift.
The third piece of the jigsaw is that most front brifters allow some degree of trim. In the case of the Red, I believe trim positions are available when at the large ring.
So if I were in your position, what I would do is to stick a piece of tape or some such on the front gear cable (e.g. near the downtube), and try to measure reasonably accurately by observation how much cable does the Red front shifter pulls when shifting from one ring to the other currently, and what trimming delivers. If it can deliver 7mm or over with or without trimming, then it should be possible to make them work together.
If you do try please let us know how it went. Similarly it would be useful if anybody who runs a Red/Force/Rival/Apex can provide the cable pull info.
, sorry for the slow response. 