Is he pretty much the most significant/influential Lovecraft scholar of all time?
Ooof! That might be biting off a bit much. I'd say he's certainly among the most important Lovecraftian textual scholars there's ever been; also that he has written quite a bit of the most important interpretations of Lovecraft's philosophy (as seen in both his fiction and non-fiction). But Joshi himself owes a lot to such as Matthew H. Onderdonk, Dirk W. Mosig, J. Vernon Shea, and even Fritz Leiber (who didn't write a great deal of Lovecraftian scholarly articles, but those he did are quite good).
Part of the problem is that, for a long time now, Lovecraftian scholarship has diversified into several different subspecies (if you will), each of which has proven of immense worth in varying ways, from the textual, historical, and politico-philosophical aspects that Joshi has done so well, to deconstructionist examinations such as those Donald R. Burleson has written (which I personally find quite fascinating, though they've stirred more than a little controversy at times), to mythic and psychological work such as Mosig and St. Armand have done, or approaching his work from the standpoint of religious studies, as Robert M. Price has... and there's a fair amount of work being done on his earlier writings for the amateur press, which is adding considerably to our understanding of various aspects of his later, more famous work. (Phillip (ghyle) has done some very good pieces on certain aspects of this, for instance.)
I'm not sure one can point to any one single person as "the most significant/influential", overall. But Joshi certainly wins that in the area of ferreting out the most accurate texts, along with revisions/alterations done in various printings by Lovecraft, etc., providing marvelous insights into how meticulously Lovecraft approached his fiction, in order to convey extremely precise nuances in meaning and emotional response. This has, indeed, led to a reexamination of Lovecraft by literary scholars in general, and a rethinking of his place in American letters.... So, on that level... if Joshi isn't, he's darned close....