I don't think Evangelion would ever have been a breakout hit, per se, like DBZ, but depending on the circumstances it definitely could have had moderate success.
Also, Eva is much more, for lack of a better term, adult-themed, thematically complex, and sexually weird than Pokemon, One piece, etc. This certainly would make it less universally popular as a cultural export.
I can't help but feel you're significantly overestimating the "average familiarity" here.
And I'm pretty sure at least Pokemon is well entrenched into popular culture. Death Note and One Piece have had Netflix series, also indicated a good amount of penetration in the average market.
I recognize most of the names you mentioned, but haven't watched any of them other than to check if they interest me.
Obviously Pokemon is better known, but other than that it's going to depend a lot on age group.