It being able to shoot down any ships or missiles coming up is certainly a possibility. But we never actually get to see it. Plus everyone on the planets just seems to be standing around helplessly, wondering what's going on rather than actually taking action (even at Starfleet HQ, we see no ships going up or, for that matter, ships being shot down).
As for 'current-day' ships not being strong enough to take the drill out, I don't quite buy that. A rather simple phaser (not sure if it was one from the future or not) was sufficient to cause some major damage. So I figure ship-based phasers or torpedos or missiles, for that matter, should be enough to get the job done.
Don't get me wrong, this is something that doesn't bother me all that much, really. I just think it could have been done more elegantly and seem more plausible. A lot of it seemed to be part of the usual wanting the Enterprise and her crew do it all.