GTa 5 lobby but for the chosen ones?

My question is whether I can have a private session in GTA only for players with an invitation but if I leave the game that they can still stay in and if I'm not online, that these players can still play on the server with the invitation is that somehow possible for the Xbox?

I do not think so.

On the Playstation, I first had to load it into offline mode. You can choose how you want to switch to online mode.

Invited players only,

Only a certain crew

Just "normal" online

If you leave this session everyone can stay