Yup, they do. My boyfriend was contacted by a third-party recruiter working with Palantir a few months ago, and he starts work there in a couple weeks! To answer your second question - generally, I really, really dislike third-party recruiters (I'm an internal recruiter). The only reason I'd work with one is to have an advocate on your side to keep the process moving along. Sometimes companies can be slow, and if you're working with a third-party recruiter they'll bug the company to move forward on your behalf. That being said, if you can just apply to the company directly, that's what I'd do.