Yes and no. While F, B and A designations are all fairly fluid, an A aircraft is usually one whose primary role is close air support, ie precision strikes on targets that are engaging, and thus very close to, friendly troops. To do this you want an aircraft that's maneuverable, not too fast, (usually) lightweight and either cheap or very survivable. It actually wasn't uncommon for larger A-4 pilots to be unable to reach certain switches with the canopy closed because the cockpit was so small. Meanwhile the A-10 is probably the best fixed wing CAS platform ever built and can get shot all day long and keep flying.
On the other hand, the F-111 is big, fast, expensive, carries a ton and can't maneuver to save its life. Back in the 1970s, if you wanted to do CAS with an F-111 you would have found yourself overflying the target at 150-250ft at around 250-300 meters per second, while your Nav tried to drop a dumb bomb without hitting friendlies only perhaps 100m from your target. Good luck with that. And good luck if your complicated swing wing system takes a bullet, because your threshold speed will probably set a land-speed record. Probably more accurate to call it a bomber, although it's at the blurry edge of the three designations.