Yes, it does. Make sure arm is unloaded hold the arm with shooting hand NOT in firing position so the grip safety is not depressed. Then - slowly so you can see it all - move (rack, open) the slide to the full recoil - all the way back position and note that the slide depresses the hammer into contact with the safety.
Alternatively, make sure arm is unloaded: Hammer down, thumb cock the pistol and note the hammer (can) contact the grip safety.
Among other things, the hammer depresses the grip safety allowing the hammer to be lowered at need.
No. Removing the 'tang' part of the grip safety will not allow the hammer to over-travel. In short, the mainspring and mainspring guide make that impossible. (One has to detail strip the pistol to 'see' this.) However, removing the tang will allow the hammer to impact the web of the hand.
I've never done that, but I rather think it to be unpleasant.