UAC prompts should only happen in the following situations:
- the program was explicitly invoked to run elevated (i.e. Run as Administrator)
- the program's manifest explicitly says that it should run elevated
- the program lacks a manifest, and a heuristic has classified the program as an installer that likely needs to run elevated (generally for stuff like "setup.exe")
- the program lacks a manifest and is flagged as requiring elevation for compatibility (e.g. you ran it, it didn't work, you closed it, then you accepted the Program Compatibility Assistant's recommendation to rerun it elevated)
If a program runs unelevated and it tries to do something that isn't allowed, it will not display a UAC prompt - it will fail to do whatever it was attempting to do. In any case, if the prompt DOES appear, then the only thing Windows knows is "the program wants to run with increased privileges"; it doesn't know why.
There is one notable exception, though - if a program tries to write to its own installation folder (or a registry key in HKLM), then Windows filesystem/registry virtualization kicks in and redirects it to a user-specific location so it won't actually require elevation (and subsequent read attempts will give it a combined view of the install folder and your user-specific changes). Of course, this doesn't apply if your program is manifested as UAC-aware, in which case the operation will simply fail (and you should've also manifested it to require elevation).