I could easily see Node persisting for years to come solely based on the "run Javascript on client or server" feature. It is pretty compelling and for new developers why wouldn't you just learn Javascript and skip the server-side languages.
If running JavaScript both in-browser and via Node on the server let you write a distributed application and automatically handled things like marshalling the data to get from one side to the other, that would be a strong point in its favour.
As it is, I'm not so sure. Developers having familiarity with JavaScript and being able to work on both sides is still obviously an advantage, but I suspect for most projects it's balanced by JavaScript actually being a fairly nasty language to work with.
I've never found any truly compelling reason to use JavaScript, except for "if you're writing front-end code for a web app then it's what you've got" (which is obviously not strictly true, but is close enough for most practical purposes). That argument doesn't apply on the server-side, though, so I'm not sure what is going to sustain Node as dedicated server-side languages evolve or new ones appear over time.
Personally, I don't find JS to be a "nasty" language... I think it gets that reputation because some of the constructs take a while to wrap your head around (function scoping, closures, 'this', functions as first class objects and all of callbacks/event-emitter/-type patterns that come along with it.), but the nice thing is, you can do a lot in JS without coming near those (think jQuery)... and later, when you get sufficiently advanced, you learn that the things you thought were ugly, are actually what makes it beautiful and powerful. - JHMO
They won't touch Go with a ten meter pole, so no. Go won't cause Node to dry up.