Don't trust a robot vacuum on shag.
Probably not. Thick shag rugs are basically a trap for most robot vacuums. The long fibers tangle around the brush roll, and the cliff sensors often mistake the deep pile for a drop-off, so the robot either stops dead or tries to climb over and gets stuck.
Some high-end models with “self-cleaning” brush rolls or advanced sensor mapping might handle it better, but even then it’s a gamble. The cheaper ones will just give up and beep at you.
If you’ve got a shag rug, save yourself the frustration and stick with a manual vacuum for that room.