I can't really say it was anything like 'Family Guy'. 'The Critic's pop-culture references weren't only rooted in the characters' personalities, but they were also facilitated by the fact that the lead character was a film critic, thereby allowing a viable avenue for aforementioned references.
'Family Guy' is more just the Griffin family making random asides that are neither rooted in character nor allotted for by the show's context.
Seth MacFarlane definitely owes a lot of his humor to The Critic, in any case. Even when Family Guy was vaguely funny it borrowed heavily from both style and substance, and look at his pre-FG shorts as well.
Of course, today, MacFarlane's "humor" is just a ridiculous caricature of itself, all the aspects which made it at all likable having been whittled away. The cream filling might be the best part of an Oreo, but you still need the cookies to make it worthwhile.