triock: Well, Steam offers an offline mode, so once you download a game you can play most games without internet connection.
tinyE: I don;t even care about a client right now just so long as I can lose it
during gameplay. If they want my saves and game data I'm being caring about that anymore so fine.
I just remember years ago trying to play Diablo 2 on BattleNet and my character kept vanishing. :P Of course that was MP.
Depends on the game not the service or the providers client.
Most the indie shit? No problem.
Stuff that's on Steam & GOG? Almost always identical. (Like the Desktop Dungeons I traded for & loving... doesn't care if you have a net connection or not.)
"AAA" is where you might have problems. Take Call Of Duty: Black Ops 3. It has an online & offline save. If you loose connection while you're playing with online save it saves to the last checkpoint but then you can't access it & your offline save if probably further back. I almost recommend using offline save first with that sucker.
Metal Gear Solid 5 can be played offline but you'll be unable to obtain the highest tier equipment; I refuse to give into konami's sheet & play it completely offline. About once every 2 weeks the DRM demands I send some kind of code to their server to verify my PC. I assume it contains encoded stuff like what my PC is, when the last time I played is, if I have an internet connection, etc. Very dishonest stuff. Granted the multiplayer in MGS5 is decent... but I haven't played much.
Some "AAA" is just fine too. The Final Fantasy X/X-2 HD Remaster is still one of the best RPGs around &, as far as I can tell, has no DRM & doesn't care if you have a net connection or not. I have it blocked with a firewall.
In fact I think that's what I'd advise... block every game with a firewall to start unless you specifically want the online features... because then if your net connection drops your game will never even know.
There's exceptions to that too though.... like Grim Dawn. Requires access to LAN IPs even playing offline. Pain in the butt to setup depending on which firewall you use but doable. (My GD is GOG... so it's the same.)