Yep. It would be the same as Doflamingo or Katakuri's awakenings.
Currently, as a Mythical Zoan user, Luffy has special properties to his awakening. He can punch someone and turn that part of their body into rubber. No other awakened fruit user has done that, but as a Paramecia user he would be unable to do it. What he would gain, though, is the ability to control what the surroundings do.
As it is, Luffy can change the physics of a person he touches and the ground he's on, but he can't change their shape and control them with his will. For example, he can't touch a building, turn it into rubber, and then make the rubber attack people like an extension of his body. Paramecia users seem to be able to do that, but only some of them. Law and Kidd's awakened abilities allow them to apply their ability to something other than their own body, but they aren't applying it as if it were a material thing. Their abilities are immaterial, so what they do is change the immaterial properties in a localized area; K-room and R-room apply the operating room immaterial properties to a knife and to a space and Assign applies immaterial properties to two separate targets in the form of magnetic polarities.