Does registering with a specific political party help that party in any way?

I'm an Independently-minded voter. I vote for the candidate I think is best; I don't really care about their party. It would probably be most accurate if I registered as an Independent or "no party affiliation".

But let's say that I liked a certain third-party, call it Party X. Would me registering with a Party X affiliation benefit Party X in any way? I know what benefits would be in it for me, mainly that I can vote in their primaries, but would it benefit Party X? For example, does Party X having more members give them access to certain things, like various government programs or funding, or enable them to do things they wouldn't be able to do otherwise, or give them some sort of advantage?

Ignore the fact that they would probably see an increase in donations just from having more members, and that they would gain more visibility in the media. Would there be any benefits in it for them just by having a larger membership base?