I highly doubt the trans is heating up the coolant a noticeable amount to warm the engine up quicker. There's not a lot of flow through the trans lines compared to the amount of coolant in the radiator. Plus you'd have to be driving hard right after a cold start, getting the torque converter working to heat up the fluid. It works the other way, the coolant cools the trans fluid. The coolant is the coolest liquid, that's why oil and trans lines go into the radiator, those oils are a lot (or can be a lot) warmer than the coolant is, at least in the radiator.
If you have a larger than factory auxiliary cooler, you're probably fine bypassing the radiator but I don't think it will do much to help your cause. Though, if you prove me wrong, I'd like to know about it