Mine's not a true SAA but I'm told it's a close replica, and it advances the cylinder at the end of the hammer pull.
I found that if I hold the trigger back (like we presume Baldwin was doing) and cock it it will get the next cylinder in line with the bore somewhere between the half cock click and full cock, and would, I presume, fire if you dropped the hammer. It also doesn't advance the cylinder until the second half of the hammer cock, so if the round was already under the hammer, and the trigger was held back, the hammer would fall on the round in the chamber. Whether the hammer would have enough force to set off the primer from a quarter or third cock, I have no idea.