The problem I see, then, if you're confident your setup can take the voltage, will be in charging the batteries. You can't use your original drill charger if you make your setup run at 15.6v (what 13 cells nominally adds up to). You will need a smart charger to do that. So next question is, what charger do you intend to use?

My advice here might be to stick with the tried and tested 12v, and move on in due time. You definitely won't be disappointed by the power of 12v drills at their designed voltage. If you eventually feel like taking it up a notch, you'll be beyond using the cells that come with drills anyway, I'm sure.

That said, we didn't completely follow the trodden path with our first robot, and we probably learned more than we would have if we had, so it's your robot and your call. :)

Also in regards to whether overvolting is a good idea or not, it is and isn't. It is in that the power benefits are marked, but it isn't in that reliability suffers.