Yes. The Sony A77 still uses a mechanical shutter, and during 12 fps burst shooting it is physically cycling for each frame. What the SLT/translucent mirror design changes is the mirror mechanism, not the shutter itself.

Instead of a traditional DSLR mirror that flips up and down for every shot, the A77 uses a fixed semi-transparent mirror. Part of the light is reflected to the autofocus system and the rest passes through to the imaging sensor. Because the mirror does not have to move, the camera can shoot faster and maintain autofocus more easily during bursts.

The A77 can also use an electronic first-curtain shutter setting, which pre-opens the mechanical shutter and starts the exposure electronically. This helps reduce shutter lag and noise. But the camera still relies on a mechanical shutter overall for normal still capture.

So the short answer is: fixed mirror, yes; moving mirror, no; mechanical shutter, yes.