Depends on a couple factors:

• Will the game play without a firmware update?
• Will the game play without a game update? (deliberate gate, or by presence of game-breaking bugs)
• Even if previously updated, does the game arbitrarily enforce a persistent connection?

The first one is usually the catch. On Xbox, you have to download the firmware update, it's not on disc like Nintendo and PlayStation. If you haven't updated your system in a while, you usually can't play newer games. (MS has/had a workaround for this, where you could download firmware from their website and install it via flashdrive. It's something, but still weak for needing Internet.)

Needing a game update happens semi-commonly too, but it's certainly the exception. Something like 80+% of games probably play fine without one, even on Xbox.

Single player games forcing you online all the time is pretty rare, but happens. Some especially spiteful, incompetent, or cloud-brained pubs will do it from time to time.