By saying this I'm also going to assume you don't play very many games on it or use it much.
I'm in another city working for some months already... so I have to take my PS4 and use RemotePlay to play/display via my notebook using a small 1m ethernet cable (somebody give me this ideia it is flawless with near zero input lag from the RemotePlay).
I only hook it on internet very few times... the last one was yesterday night and before that is was in middle December.
I'm having no issue playing my games except for three notables for obvious reason: GTS, Destiny 2 and SFV.
Everything else is playing just fine without internet.
So unless it is an multiplayer or online required game you won't have issues playing offline with PS4.