Well, I'm looking at a much more tumultuous relationship than that of Scott and Logan. For example, I wrote in a brief physical altercation when Logan and Gambit first meet (which happens to be at a bar). Logan openly opposes Gambit staying at the mansion, but is overruled by Storm because Gambit saved her life (an extremist shoots her, but Gambit throws an explosive card into the guy's gun hand, so Storm ends up shot in the arm instead of the chest). Gambit doesn't really want to become a "student", but Rogue talks him into sitting in on a couple classes, one of which is a self-defense class taught by Logan. The class is taught in the Danger Room (virtual reality, so nobody really gets hurt), where Logan and Gambit duel. Though Logan wins, they have an excellent fight in which they earn a degree of respect from one another.
I don't think this relationship would be a whole lot like Scott/Logan. In the beginning, Scott and Logan had more of a mistrust than a hatred; and I'd hardly say their later relationship was based on respect. I'd say it was more like they grew on each other, and grew fond of each other and their opposing personality traits. With Gambit and Logan, you'd NEVER see them crying in each other's arms; but you'd see certain undertones of admiration in their interactions. Gambit might in some ways respect Logan's authority more than he does with the others, while Logan might be less bossy with Gambit than he is with others. Their relationship would be pretty much all about mistrust and respect (which may be somewhat paradoxical), without the same love you saw between Scott and Logan.