No. This dynamic does not exist in the show. No one wants to be like Jerry. Jerry doesn’t even want to be like Jerry.
Morty is the uncertain, fretful, anxious character that balances Rick. That’s the whole point of his character; the fun is watching him grow as a person and in watching Rick grow as he becomes less like himself because of his fondness/need for Morty.
Jerry is superfluous except as a source of stupidity and as something to hate; he is a permanent and irredeemable foil. And again, in real life, people do not hang out with Jerrys on purpose: they are a drag.
ETA: Nice edits while I was typing my post.
IMO, no.