Um, kinda, but the clutches in a ATESSA transfer case are WET clutches like the ones you find in a motorbike, so slipping isn't really an issue for them, its normal operating proceedure.
There is an actuator (visible from the rear where the hydraulic line enters) that contains a plunger that acts on the clutch plates and takes drive from the chain emerging from the rear of the gearbox and engages them progressively as the torque requirements demand as dictated by the attessa pump (above the diff)
And the answer to your question about the syncro button, is no. Well, that's just my opinion, but unless you are having black ice type traction problems, its better to let the ecu's figure it out themselves. Just like when you put your foot flat and the trans (in a S1 - nfi idea about the others) automatically goes into "sport" mode, and the air con clutch disengages, the cars are pretty intuitive and you have to be trying pretty hard to confuse it.