Increased squad size causes an increase in enemy squad sizes in tournaments, but I don't think it impacts map encounters at all. I think map enemy size is a function of the distance from your city(the further away, the higher they are) and the advanced scout techs (reduces difficulty of all unscouted provinces). Barracks upgrades only does 2 things: early game it adds more training slots up to the max of 5 and it makes them train faster. You didn't ask about armories, but upgrades to armories increases the number of units you can train in one training slot.