To a point they will still function, until they don't. I'll admit in auto body I've shaved one flat down to make nuts fit, but that's mostly sheet metal and mounting brackets. Depends on the strength needed. There are cases where the nut has enough friction against the part to tighten without a backup wrench and strength isn't an issue, there I'd say its okay without flats. Then it needs to stay tight and not come loose. So sure, I've done it, but I wouldn't recommend it on every case, just the cases where it's safe and secure to.
Edit: Sometimes, I'll even tack weld a nut onto the work to ensure I don't need to back it up with a wrench on assembly. YMMV.