Well, Dragon apparently uses a hand-to-hand fighting style (Ryusoken, which he probably taught Sabo), so it's possible... although I feel that Dragon went in a different path very early (their styles seem to differ too much), so I personally don't think he had any training with Garp besides being thrown in a forest and getting kicked around as a kid like Luffy or Ace.
Kuzan implies that he had Garp as a mentor (although he might be referring to Luffy and Ace in chapter #1087, yet his statement would make more sense, following the logic of the flashback, if he had multiple apprentices turning on him), but maybe he also trained with Sengoku or someone else in his short time in the marines (did he learn Ryusoken from someone or did he create it from scratch? Garp doesn't seem to have any proficiency for it).