Stopping a brushless DC motor in a specific position
I think if the speed controller was completely off, and you connect it to the battery, it would snap to some position. However, depending on the number of poles in the motor, you might find that it's not just one of six positions, but one of a multiple of six positions. In other words, you could get it to snap into line with one of the phases, but there may be multiple points that represent that phase, and the motor will likely just seek the nearest one.

Of course, if the ESC were to become activated while you had this alternate connection in place, you'd probably smoke at least a couple of the MOSFETs, so, hazard there to worry about. As long as it's off though, I don't think the speed controller would be harmed, b/c if you think about it, those MOSFETS routinely switch the battery voltage to make approximately 3-phase AC out of it. There should be protection diodes in the 6-way bridge that will protect it from the inductive kick-back when you break your alternate connection, too.