There is no "Swarming" as Total Warfare might recognize it, so most of the answers to this line of questioning can be solved by looking at it purely as the Alpha Strike rules explain, rather than by what you might remember from other rulesets.
In order to perform an AM attack, the Battle Armor unit must be adjacent to the target 'Mech. This, almost by definition, makes them vulnerable to a physical attack from the 'Mech in question. Mind your firing arc, though!
Under Alpha Strike rules, units are only protected from ranged attack from the unit they're adjacent to (I play mostly hexless, where this is much easier to determine). Units that they are not adjacent to can shoot all they want. Remember that units do not block line of sight.
Battle Armor conducting an AM attack are still "merely" conducting an attack. They do not occupy the same space as the target unit, and are in no way considered to be on/swarming the unit.