First a general answer: Yes, drilling a valve hole to make it larger is fine. It's done all the time in bicycle shops.1
I've seen lots of rims crack at the nipple holes, but I've rarely (if ever) seen a rim crack at the valve hole. It's not a problem.2
Of course, in order to do a good job, one should use a sharp drill, not apply too much force, clean the hole with a file afterwards, and make sure there are no shards or shavings that could damage the tube.
Presta valves need 6.5 mm holes, Schrader and Dunlop valves need 8.5 mm.3
Now to your case: Since the top part of the valve passes through the valve hole, the valve hole is obviously made for Schrader valves.4
But maybe the valve is a bit thicker because of the rubber, or maybe the valve hole is a bit too small. Either way, you only need to make the hole a little bit larger. (I'd measure the hole and the valve with a caliper to get a better idea of what's going on.)
I guess you need to make the hole at most 0.5 mm larger, probably less. You might even be able to do it with a file without too much effort. But if you want to use a drill – sure. Just make sure you get one with the correct diameter, i.e. at most 0.5 mm larger than the current hole.
(I guess you could also remove the rubber from the valve, but to make sure the valve really goes through the hole you'd probably have to remove the rubber all the way down to the tube, and then I'd worry that the whole thing isn't airtight anymore or even comes apart. And you'd have to repeat the operation with each new tube that has a similar problem. Making the hole larger seems like a cleaner solution.)
1 Maybe more so here in Europe where Dunlop valves are quite common, which have the same outer diameter as Schrader valves. A rim with a Presta valve hole needs be drilled to accomodate the larger diameter.
2 Well, with an extremely light rim, e.g. a narrow 622 rim below 450 g or so, I'd maybe think twice. But generally it's fine.
3 See e.g. Ryde's specifications here and here.
4 It's almost certainly not a Presta valve hole, as some commentators seem to think.