The amount of clicks to get somewhere has already been disproven many times; so in light of that, its good as long as the user gets the sense of going forward.
That being said, I think just "sign up" is enough, as, like you mentioned, you can give people several options to register on the following view (not limited to linkedin even). I think the real question is, how do you convince people to click on the register button, because, if I don't trust the site, I'm not giving my personally info, let alone my linkedin.
What you can do, however, is make it very convenient to register, for instance, at the bottom of each site or as a bottom banner on your "sales-pitch" pages (the pages that explain what benefit the user has from registering).
As always, it depends on your use-case; sites like FB/LinkedIn need users and lots of it, so they slap you in the face with an easy to use sign up process :-), but they have a different use-case than StackExchange, for instance, that wants to share great information in the first place :-)
You can definitly A/B test this one and see if it makes a difference.
interesting reading material: