well, sort of.
woodworking gurus will tell you that end-grain wood is weak. hardware store dowels are end-grain wood. the truly "correct" way is to make a "plug" out of cross-grained wood, where the grain is perpendicular to the stick itself. (of course, this is much more of a PITA.)
an end-grain dowel of some kick-ass hardwood like oak or maple should be OK, especially compared to a basswood body, and an originally end-grain strap button hole at that.
i'd go bigger, though, like as big as the button will cover (3/8", maybe) and a couple of inches deep. otherwise once it's drilled out for the button, you've got a thin layer of end-grain wood inserted in a smooth-sided hole, held in place by glue alone. there's little structural strength there.
with the far easier toothpicks-and-wood glue method, the new wood gets compressed against the rough thread remnants of the old hole when the screw gets cranked in, allowing the thickly applied wood glue to dry strongly, creating cast-in threads for the screw.
as for JB weld or other such epoxy-type stuff, since the wood-glue method is way easier, strong enough to break the screw head off if over-torqued, and poses no risk to the surrounding finish, what's the point?
