I opened my Gox account early in 2013 and verification was not required for BTC deposits or withdrawals. They even stated so in this press release:
https://www.mtgox.com/press_release_20130530.htmlWhat I have learned is that Gox will flag your account if your IP is used to log into more than one account. So suppose a friend logs in from your home IP, or you log in from a shared work IP... too bad. You will now need to verify. This is what happened to me.
Apparently their current policy is to require verification for all new accounts, but older accounts may still be ok if you haven't been flagged.