It looks as if that bridge has a constant diameter hole of about 7 mm. Is that right?
If so then yes theoretically you should be able to drill it for a recessed brake nut. What Mud says it true - you'll need a drill that will fit into the very small space between the bridge and the back of the seat tube - and this may be a real PITA.
I have seen folks drill the hole from the outside so that you end up with a through hole of 8 mm and I suppose it would work but the hole wouldn't locate the brake bolt well and the nut would do all the location. Would this be an issue? Maybe but it seems like it would work. It would certainly be much easier to drill the bridge from the outside.
Is that frame set up for a LRC? It's hard to tell but looks like it might be.
Dave