The rule is different for H1 and L1
It was like what you said a few years ago, but CIS changed the rule in 2003(?) to allow H1 and L1 (maybe O1) visa holders to use visa instead of AP.
Yes, you can still extend your H1B after you use AP. You can still work for your originally employer without EAD. In another word, your H1B is still valid.