Can I update my Nexus 7 from 4.2.2 to 4.3 and root it without losing data? Device: Nexus 7
Android: 4.2.2

Can I upgrade my Nexus 7 to 4.3 via OTA, then re-root without losing data? I used a procedure of this sort to root originally, but I don't know if it is generally possible.

Note: I did not unlock the bootloader when I last rooted.
NO. 

Updating from 4.2.2 to 4.3 will retain your data, but this will make you lose root. To root, you would need to unlock the bootloader, which will almost always require a Factory Reset (thus, you lose your data).

So, I suggest to back-up your user apps and data with Titanium Backup or something similar.