Yes, you can do all of the above. I currently have KT66 in one side and TS 5881s in the other. At one point, I was running 6L6GC-STRs in one side and 6L6-WGCs in the other. At one time, I also had two different types of EL34s. As long as you bias it correctly according to the rating of the tube, you're good.
That said - running a quad of the same power tube in the Renegade isn't going to really do much for you. You'll get about 15W more power by running Tube Mix in the center versus fully to the "6L6" or "EL34" sides. You're not going to get the 100W you get with standard type amps that use a quad - you'll get 65W versus about 50W that you get in the fully left/right positions. So, I would be more inclined to run two different pairs of 6L6s - that way you can blend the sonic characteristics of both.