Depends who you're talking about. Anyone that was a kid in the 90's has a pretty good chance of encountering some kind of X-Men media thanks to the animated series; whether it's the show itself, the tie-in merchandise that was everywhere for a few years there, or the various console and arcade videogames.Among comic fans, yes, but not to the general public. I remember when the 2000 movie came out many people not having heard of X-Men at all.
That demographic includes myself, who was very much not a comic book reader at that age, and yes, the yellow suit is still the one that comes to mind if someone were to ask me to picture "Classic Wolverine".
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