In one word, DEFINITELY!
Google and Facebook, aren’t looking for IITians or NITians. They are just looking for people with skills which would benefit them. Now coincidently (or maybe not) these qualities happen to be with some IITians or NITians.
But that doesn’t mean that they have a preference while recruiting from IITs. Even here, in IIT Delhi Google conducts its own entrance tests and more often than not ends up selecting nobody. This is because they are looking for the best engineers in the field of Computing, Coding, Analytics, etc. Now to be fair if you were in Google or Facebook and were the head of the HR (Recruiting Division of an organisation) you would obviously prefer to go the IITs or NITs because they have credibility as they did secure the top ranks in the National Level Entrance Examinations.
But that doesn’t mean that if you were to independently apply, Google/Facebook would unabashedly deny your application. The correlation between IITians and Google and Facebook is pretty strong, but as you may know or if you don’t allow me to lift your spirits, Correlation doesn’t equal Causality.