I can't fathom what the general consensus (if such a thing exists, and I intimately hope it doesn't) was when James came fore, mainly because there wasn't an online community to draw opinions from. It seems to me general high consideration can't be really detached from popularity, and James appeared at a time the 80's big guns rock tenors where going out of fashion and the"new" popular trend was guys like Cornell, Staley, Vedder, etc.
Personally, when I first listened to James, I thought he could be a cocktail made of Kiske, Mercury, and Perry, but I never assumed he was going to establish himself in some general pantheon, mainly because the genre he was involved in was quite nichey (if it is a word), and a bit late fad-wise (ditto).
All is relative to times and perspectives anyway. For example, I used to idolise Coverdale, while my father - who had lived through hard rock's genesis - would stubbornly insist he was worth half Paul Rodgers.