I'm connected to the imap google server for my emails, read and deletions do work all be it slowly. I have around 10,000 emails in the last three months synced to my phone so that may be causing slow down. But if I force a sync on my phone the changes do appear on my PC eventually.
Sorry this isn't any help but as far as I can see there isn't a setting for this, you either sync emails both ways or you don't as far as I can see.