Also, as far as a pokemon based on one animal (eevee, a fox) evolving into a pokemon of an entirely different species, I know this is also definitely possible as well. For example: remoraid (fish) into octillery (octopus), eggsecute (eegs) into exeggutor (some pineapple tree thing), clamperl (clam) into eel pokemon, and lets not forget feebas and magikarp.. xD
I'd also like to add that I don't really find anything very reptilian about reshiram being that its so furry/feathery, and even the hydreigon line has some fur on them. I still think they could pull off a dragon eeveelution with fur.
I know it's not really furry, but let's not forget Flygon. Weird crab to a giant dragonfly-ish thing. No I think the dragon type in Pokemon can mean a lot of things. It can mean actual dragons (Salamence, Druddigon, Dragonite, Hydreigon), Reptilian like (Haxorus, Garchomp), but recently a lot of legendaries are given the dragon type as a dual type with whatever element they are associated with. Palkia, Dialga, Giritina, Reshiram, Zekrom, and Keyrum all are semi dragon type. Those are all of the mascots of the main series non remake games of the last two generations. Based off of this, I think Pokemon with the dragon type are usually powerful, and are almost mythological. How all of that translates to an Eeveelution I have no idea but don't count on a dragon type.