No.
Luffy is Garp's copy.
This doesn't imply anything. OP isn't saying Luffy isn't related to Garp. Hes just saying that Luffys mother was Garps daughter, while Dragon was just taken in and fell in love with his daughter.
Aka, the really point of the theory is that Dragon was related to Rocks, but was Garp's son in law after the fact. We'd know soon enough, because either he would have been with Rocks on his ship, or existed om God Valley because Rocks lover was a Tenryuubito or something.
Basically the tree would look like this:
Grandmother - Rocks | Garp - Grandmother
\ /
Dragon - Mother
\ /
Luffy
Not saying its possible, but recall that Oda has never let Garp call Dragon his "son". Hes only referred to him as Luffy's father. By contrast, Garp has called Luffy his "Grandson".
It seems Garp is more offended by Luffy being a pirate, than Dragon being a revolutionary, which seems to be way worse in One Piece's world since actively trying taking down the WG seems to net Dragon to be the world's most dangerous/wanted man. This makes sense more of Dragon wasnt Garps blood.