No, main sensor is used for Live View, the mirror is only used for AF. The AF system needs to be precisely aligned with the sensor. On the Alpha 55/33 this is much easier to achieve because there is only one non-moving mirror, while on a traditional DSLR there are two mirrors, both moving theta project the light to the AF-sensor.
The three digit Alphas having the Quick Live View may have the problem you describe.
I'm not in possession of either Alpha 33 or Alpha 55, so my response is based on info on the web and not own experience.
I have a possibly paranoid concern about this type of camera. The image in the viewfinder or on the rear LCD is produced by a secondary sensor located where the pentaprism would normally be, not by the main sensor used to capture the photograph. That's one of the reasons this type of camera needs a mirror. It seems that if there is even the slightest misalignment of the secondary sensor or the mirror, the image in the viewfinder could be in focus while the captured photograph would be slightly out of focus. This is the same thing that can happen in a traditional SLR if the focusing screen or mirror is slightly misaligned. In contrast, most cameras with live view use the same sensor to display the live view and to capture the photograph, so if the live view is in focus the photo will be in focus. I guess in practice the Sony approach probably works fine, but you're counting on them to align everything in the camera perfectly at the factory.