OCNC -
I think this could be done - obviously a mill would be better for rigidity, but -
The problem you will likely have is that the tool is going to grab on both entry and exit - you know this obviously. A carbide tool is likely going to shatter on a drill press unless it is a hefty drill press with a stout spindle. Using cobalt tools sounds reasonable as they seem to be more forgiving to abuse, and a ball end mill is worth a shot. Watch your speeds and keep the tool and material cool somehow - stainless can work harden like a Swedish secretary.
The other thing you could do to help is use a spot drill - a drill with almost no flutes - and use a piece of wood as a drill guide. The bad thing is that spotting drills are typically only two flutes, but maybe you can improvise somehow using some sort of guide.
...just some thoughts - likely not all that helpful. Sorry.
Scott
Consistency is a good thing....unless you're consistently an idiot.