I've never had any issues with offline mode yet, except for one time when a Steam Update set all my games to Download- Paused, and I could play them while online, but not offline. My offline mode has currently been running for about two weeks now. :P
I do know that a lot of other people have issues with offline mode being totally broken, though, so it seems to be different from PC to PC.
Yeah my PC is also verified. And steam is always running.
T A N S T A A F L
The thing that gets people with Steam's 'offline' mode is that you still need to be online at the time of login, once you've logged in and gone into offline mode you no longer need to be connected. So as long as you don't close Steam you can stay in offline mode indefinitely (well not 100% sure if there are some limits).
Unfortunately if you are trying to start Steam and you don't have an internet connection you are out of luck.
Could work, but I wouldn't. To much risk & hassle and steam games aren't that expensive anyway.
I download and update my STEAM account from the office (uncapped) and play my games from home where I only have a 3G connection.
I just copy the STEAM cache files to my home PC.