Does any Buckley besides William F. really qualify as a prominent conservative? I think James(?) ran for some political positions in New York(mayor?), but I haven't really heard of anyone else. Bill's son Christopher is a well-known writer of fiction, but not regarded as any sort of conservative hero.
As for WFB himself, I think the conservative reaction of the 1960s to the early 90s, finally manifesting itself in Reaganism, would have taken shape more-or-less the same way no matter who was articulating the relevant values. And it would still be a coalition of free-marketers, states' rights rebels, foreign-policy hawks, and religious conservatives. I don't think Buckley himself made any decisive contribution to any of that coming together.
I'm not even sure he had much influence over the way conservatives are viewed by the general public, largely because he wasn't that well-known to the general public(compare, say, Phil Donohue), and his style and mannerisms were pretty atypical of right-wingers generally. If you were to ask your average person to envision a right-wing talking-head, it probably wouldn't be a foppish Yalie with a mid-Atlantic accent.
MAYBE Catholics are slightly less respectable among conservatives, without a papist being the main intellectual spokesperson for the cause, but even then, I doubt it: Know-Nothingism wasn't likely to survive into the mid-20th Century, regardless of the affiliations of leading conservatives(especially once the religious right got going in the 1970s).