So, to use the rules in A&A Europe 1940, Second Edition, (AAE '40 SE) as an example - the current rules do not call for rolling from the 1 column to the 4 column on the battle board. That said, those rules do call out certain actions as taking place before others. The AAE '40 SE rule book (which is available, along with all the current A&A rule set, at avalonhill.wizards.com/rules), pages 16 to 21, describe how combat goes down in the new rule set.
Don’t assume that combat works the same as back in the Milton Bradley-era A&A. First, the bombing raids happen - with the counter-fire from AA Guns and Fighters taking places before the bombs start falling. Then, the Amphibious Assaults take place - first the naval battles, then the ground battle (assuming the naval battle is successful for the attacker). After that, the “pure” naval and ground fights take place. In the details for naval battles, either before an Amphibious Assault or just as a part of seizing a sea zone, submarine, their casualties, and their continued presence on the surface is taken care of in a special part of the naval combat round (assuming a destroyer on the other side of the fight hasn’t neutered the submarines’ special abilities).
But yes, in a single round of combat, every unit eligible to shoot can be rolled up all at once, provided there is a way to tell the infantry hits from the fighter hits. Whether that is important or not, and whether the people you are playing with would like to do something about that, is up to you and them.
-Midnight_Reaper