Re operations in strife torn areas like Somalia or Serbia, or in cooperative military exercises like Desert Storm or the Iraq war & Afghanistan , has Mexico ever contributed manpower to these types of exercises and/or operations?
According to Wiki:
So no, the laws of the country prohibit using the military in that way.
Despite the cite, the Mexican army helped out post-Katrina, and entered our land for humanitarian aid purposes.
I wonder how many deserted? 
Searched various news archives: none, apparently.
There was controversy among the Mexican opposition at the time of the mission, but President Fox argued that the restrictions on foreign deployment are for “DN1” missions (combat/security operations), not for “DN3” missions (humanitarian relief), and the specific case was sympathetic enough to make it stick. (So, you see, the debate over Presidential authority to act as CinC w/o going to Congress is not exclusive to us). So I suppose that the standing policy right now is, no to going anywhere to risk getting shot at w/o a formal declaration of war, yes to diaster relief in their backyard. From what I read, it seems the policy has also been cause for debate, in that it keeps Mexico from participating in UN peacekeeping.
To answer the question, in World War 2 a Mexican air squadron saw battle in the Philippines.
It wasn’t despite the cite, it was in the cite. It also mentions help in Indonesia during the disaster there.