Using LR Mobile to review and delete

Yes, you can do what you asked, but not exactly as described.

Lightroom Mobile has ratings and flags, so you can assign star ratings or Pick/Reject flags to any photo that's synced to Lightroom Mobile. You can't delete photos from the desktop directly from Lightroom Mobile, but you definitely can delete them with just one more step:

1. In Lightroom Mobile, apply the Rejected flag to photos you want to delete. This setting will sync back to the photos on the Adobe server. When you get back to your desktop computer and start Lightroom there, it will sync down all the ratings and flags you applied in Lightroom Mobile.
2. Now, in the Lightroom desktop application, choose Photo > Delete Rejected Photos, and every photo with a Rejected flag will be moved to the computer's Trash and removed from the Lightroom catalog.

For me, there is no difference between how I eliminate images in Lightroom on the desktop or in Lightroom Mobile. In either, I'll make a pass with Reject flags first, then check to make sure I didn't mark something as a Reject by mistake. Then, in Lightroom on the desktop, I finally delete them all at once with the Delete Rejected Photos command.