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I can assure you that the installation does not require an Internet connection and FNV is fully playable offline.
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melmovano: I can confirm that there is a problem with running Oblivion without internet connection:

https://www.gog.com/forum/general/release_the_elder_scrolls_iv_oblivion_97ff9/page19

However, I was able to run Fallout 3 and New Vegas without internet connection, perhaps the DNS was already cached here.

GOG, do we have a DRM here?
Again, let me reiterate, you can install the game offline and play it offline.