If i don't have xbox live, can I still rank up while playing offline?

No.

You can still gain achievements while playing; however, some multiplayer achievements cannot be gained unless certain multiplayer actions have been performed. If you can’t perform these actions with a system link game then those achievements cannot be gained.

If you are wondering about specific games ranking then it would depend on the game’s programming.

If your asking about rankings such as laptimes or similar things in games then no, you can’t compare your rankings with others while offline.

no

In Modern Warfare 2, you can rank up with your friends offline in multiplayer, but that does not transfer over to online play.

@sweetteaindahouse Can I still unlock attchatments to my weapens while playing offline?

@xboxfan Yes, but they also don’t transfer over to online play.