They don't make left handed drill bits in a size small enough to drill out a 4/48 or a 6/48 screw.
The point on a drill bit is not the same angle as the seat that is cut into your scope mount. So even with that method, if you drilled it and hit the seat, the mount would no longer be any good, unless you had a cutter that could re establish the taper in the seat.
You can sharpen a larger drill bit left handed, but anything smaller than 1/8 inch is next to impossible even with a drill doctor.
You can however use a small punch to peen the inside of the Allen head screw, which might give you something to grab a hold of with something else.
More than likely, the screw head was metric and you tried using a SAE Allen wrench to remove it, which would not work.
One more thing you would want to do is grind back your allen wrench to an area where it is not damaged. It will no longer be any good the way it is anyways.
A Allen headed screw / bolt has two surfaces, one that is used when you tighten it and another when you loosen it. When you damage one by over tightening, the other does not have the strength to remove the screw. A gunsmith might even have to silver solder a allen wrench to the screw head to remove it. Which means that it would not be a good idea to drill off the head.
If it is damaged beyond repair, they will have to move the holes ahead or behind the origional holes and re tap them.