I guess it all depends on how binding one considers precedent to be. If you think precedent is most important, then Aragorn's claim was probably illegitimate.
However, I think we can safely infer that Tolkien's view was that Aragorn was the legitimate heir and that the Gondorians made a mistake in refusing Arvedui. On the other hand, I think it is also hard to deny that the power vacuum had something to do with Gondor's willingness to accept Aragorn.
As a slight aside, I'm not too sure that Arvedui would have been such a great king even had he been accepted. That may have played a role in why Gondor rejected him.
For more on that click
here.