Yes, everyone trains for air to air. The hornets do a lot of it (too much depending on who you ask) but it is a core competency for them, the Harreirs do a fair amount and the cobras do just enough to be dangerous(vs both the F-5s and other Cobras and if we are lucky we get to fight the Hind out in Yuma) and the assaults do enough to survive until help arrives.
The nice thing about the air to air regime is that it is the most dynamic and challenging regime we can do and it develops flight leadership and tactical decision making better than anything else.
But keep in mind that is not nor should it be our primary focus (when was the last time anyone got an Air to Air kill?)