1. Early game you certainly can do that. Take an early game fighter-bomber, then you get the benefit of both defensive fighter cover and offensive bombing capability.
I initially liked this idea, but thinking about it some...
It doesn't really make sense as a pre-emptive buy that you bomb with until the AT plane shows up, because bombing with it significantly limits the plane's utility as an AT plane counter. It could easily be down for refuel/rearm when the AT plane shows up, if not shot down outright because they bought a fighter. Your opponent will see it in advance and can engineer these scenarios; maybe even just countering it without spending any points by flying out the AT plane when you've recently made a bombing run.
As a reaction buy, it could be useful, but so would a fighter. (assuming you've the points on hand to buy either, which is another big issue) A fighter's often cheaper, more survivable, still useful against ground targets, and way more useful against the rest of your opponent's air force than a multirole would be. Most decks don't have a ton of plane slots to spare, and the decks that bring out AT planes often have very good air sections that will put your ability to field fighters at a premium.
Something to keep in mind, though, I guess; some of my decks do have a phase A multirole and I should be mindful that I could be buying them when I see a lone AT plane flying out at me instead of buying a fighter. Bombs can be nice, and multiroles often fly a bit slower than their fighter counterpart so they might also do a better job shooting down a slow-moving AT plane.
In general, though, I'm not sure that it's a much better option for your slots and buys than just a fighter.
Are AT guns overpowered because they can destroy an armoured push?
That's not a good analogy. At AT gun can't cover the whole map. An AT gun is readily countered by units every opponent will have in droves. An AT gun can take return fire from enemy tanks; even fighting the unit they "counter" they can fairly easily be overwhelmed if the attacker achieves local force superiority.
There's a reason "AT planes are OP" is a perennial theme on these forums and "AT guns are OP" isn't, and that's because the two units don't really have a ton in common. In most regards excepting what they're designed to shoot at, they're opposites.