No, he doesn't wear any system.
It is not widely accepted, these are only crap rumours made by people who have plenty of free time i suppose. And i think some people who have hair problems simply feel better believeing that some big stars out there in the world have hair problems, too. Even it's only in their imagination, and doesn't help them in any way coping with baldness!
OK, there are some old pictures(some 10-15 years ago) of him with a bit of receding hair, but in the meantime he could have done several transplants, for example. And also he wears the hair very long and always with some sort of combover , but well styled. That indicates that he may have some very minor problems of density, or temple receding, but perfectly "fixable" with a good hair style. And maybe it's simply that when he doens't have time to style his hair he simply prefers to put on a cap.
And come on, his father is, how old, over 60, and still has decent hair, ok, pretty much receded, but you can't call Julio Iglesias bald. So his son at 35-40 couldn't be a NW6 for a full cap. Never mind that now there are transplants, there are drugs to halt hair loss, etc, so the son is obviously advantaged .
And look at his brother, he has an even fullish head of hair than Enrique. Do you think he wears a system too, come on, it's absurd.
Anyway, thinking at things like these is nonsense, i believe. It doesn't help you in any way.