Many Windows programs embed resources (such as icons) in the executable; perhaps this access pattern would be indistinguishable from what common programs already do?

I'm honestly not sure - for instance maybe the embedded resources get loaded into RAM not read from the file. But if that is the case couldn't the embedded SQLite file be marked as a resource and loaded by the same mechanism?

I'd expect reading to be fine, but probably not writing. I could be wrong though, I'm just speculating.

In DOS days AVG's heuristic detection engine had flag for programs that did write into their own binary (it was reported as +i AFAIK), but it didn't have much weight as essentially anything compiled with Borland Pascal was flagged in this way (IIRC including AVG itself).