If I'm not a host can I still record a video meeting?

You can always record a session using any number of 3rd party screen recording software that is completely independent from Adobe. For example, on the Mac OSX platform, Apple's Quicktime Player offers full audio and video screen recording. I found that much better quality than using Adobe Connect recording.

The function of starting and stopping a recording in a Connect room is a Host only function. Individuals in Presenter or Participant roles are not able use the Record Meeting function.