The only warning you should take seriously is not to spend the ridiculous amounts of money Oxford ask to train you.
Go somewhere else for a 1/3 of the cost.
The job prospects are exactly the same.
It shouldn't affect your airside pass etc there is a list of convictions which prohibit you from ever holding an airside pass and I doubt that's on there.
Whether Oxford or another expensive school will accept you is another issue. What an airline thinks well you'd have to ask someone in the HR side of things.
If you go to the States for training it may take you longer to have your visa issued but shouldn't be a problem as long as you are honest. Lie and get caught and then that's where the trouble begins...