The Roman Empire was its strongest, from a military point, when it was just Romans in it. They took in another culture's idea of fighting skill, weapons but for the longest time they did not take them into their legions. To a Roman male there was no greater honor than being in the military. They had a strong belief in duty and loyalty. Only when the empire grew and their society started to decay, only then did they take in outsiders. I believe the military stopped being all it could be once corruption in the government and society started to fall apart, not because they allowed outsiders in their ranks.
Information taken from watching documentaries and reading a lot of history.
As for the question, illegals have no business being in our armed forces whatsoever. If you are a legal citizen who was born and raised in another country, knock yourself out and join.