Well, we know that only channelers can wield TP, so presumably when channeling either TP or OP, the same "connection" is used. This would likely mean that you could not for example channel twice your natural strength by using both TP and OP at the same time. Many of the quotes by both BS and RJ support this, since this would be a major advantage to TP users.

Is it possible to use half of your power connection to OP and the other half to TP so you are channeling both, without actually going over your channeling limits. I don't know, but as has been said, due to the potential nasty interactions between the powers I cannot help but suspect this would be very unhealthy thing to do.

It also seems to me that it would pretty pointless thing to do. The major advantage in TP over OP is that there is no way for other channelers to detect it, and that it ignores ter'angreal that manipulate the OP. Seems to me then that if you are willing to touch TP at all, you are better off using it in full. No benefit in going 50/50.

Ofcourse it is possible that the DO could sense you channeling OP and deny you access to TP as a result. Or it could be that a channeler cannot split his connection to both the Dark One and the True Source which would be required to channel both. This is an interesting question though. You might want to ask BS in his twitter page about this, he might give you an answer from RJ's notes.