The microUSB port would fit but I don't think that applies to the rest of the body. In any case, you wouldn't be able to use it as a dock per-se... why not get a proper Nexus 7 dock? or no dock at all, just use a cable...
The reason for needing a dock is that I use the P6800 as an alarm clock next to my bed and I have a spare S4 dock.
I was just looking at images of the connector at the bottom of a Nexus 7 and I get the impression that they're opposite of the S4 (the curvy side of the connector is at the back). So even if it fits the dock, the screen will be facing the back!
Get a case that props up the Nexus at the appropriate angle. Or a plate holder (what the older female members of my family use to display fancy dishes in china cabinets, etc.).
Connector's backward. Nevermind, it's facing the right way, I was looking at my Droid MAXX, which faces the opposite direction. No idea if it has the right clearance, but it looks like there's a good chance it'd fit.
Again, just get a charger and a cheap business card holder frame (they sell them at Office Depot). Voil?! Instant dock! Sure, it doesn't activate 'dock mode' but hey, you're just burning AMOLED life if it's on all night... just push the home button to wake the screen if you want to check the time.