That depends on when you bought the base game. Sims 3 base games bought before sept 2012 do not have an Origin requirement while the newer ones do. You can still play offline though you just need to login.
As for your error: Make sure you have Proxies turned off. Control Panel --> Internet Options --> Connections --> LAN Settings --> Untick Proxy Server
If this doesn't help, check this thread: http://answers.ea.com/t5/Origin/Origin-Client-says-quot-Online-login-is-currently-unavailable/td-p/2069735/ or this one: http://answers.ea.com/t5/Origin/Origin-Client-says-quot-Online-login-is-currently-unavailable/td-p/2069735/