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Technically, yes. But I wouldn't recommend it.
If you look at rather old bikes, the seat stay bridge is sometimes just a drilled tube. But that was before they figured out that the caliper is pulled down and forward under braking, which will elongate the hole.
Compare with the bridge on any half-decent bike built in the last (at least) forty years.
By now, I'm sure you've guessed that this won't end well for either your frame or your boyish good looks.
That's assuming you haven't fucked-up drilling the hole in the first place. You won't get the frame under a drill press, so you'll need to fabricate a guide that sites both holes centrally over the rim, co-axial to each other and parallel to the contact point of the brake pads on the rim.
Is there a chain stay bridge? You could happily fuck that up without offending anyone (or the resale value) and mount a brake there. I'd go with a single pivot brake like a Weinmann 500 and let the flex in the arms take some of the strain.
EDIT
Predictably, Tstr has a jig so presumably drilling the bridge and fitting a brake is "approved".Which, if confirmation were needed, just goes to show what I know.
Random question but can the rear brake bridges such as that one be drilled?
Went for a run at the weekend and my right knee is now totally shagged. Would be nice to go single speed for a few weeks : /