It certainly appears to be the case. Frankly, based on what’s known about his parents, they don’t appear to have been very responsible people, but impulsive & selfish. The apple doesn’t fall far from the tree.
That’s what makes me think it’s likely.
Another Freeper posted this link to a documented timeline of the Cruz family citizenship that made me wonder the same:
http://www.scribd.com/mobile/doc/256409078/Cruz-Citizenship-Timeline-documented