Rockstar Confirms You Can Play Offline
But you need to be online to play offline. Go figure!
If you're confused, they want you online all the time, even in Single Player Story Mode. Online for them means GTAO multiplayer. Everything else is considered offline, but of course you need to be online to play offline.
If you start offline, you will need to go online and then go back offline unless you quit the game which in case you will need to go back online to go offline. Either way you will need to log in which requires verification online. You can pretend to be offline but sooner or later the internet police (LSIP) will give you 5 wanted stars, 7 stars if you also revert your game.
If your game isn't updated and you are online, you will update. If you are offline but planning to play you will need to go online if your game is not updated. Afterwards you can now go offline provided your launcher is also updated. If not, you will need to go online once more. After that you should be fine to play offline until the next day because there will be another launcher update. You can also disconnect yourself from the internet and wear a hoodie and mask, this could allow you to go undetected for months, but it's absolutely necessary to disable your webcam and turn the sound volume as low as possible to avoid detection.