Is it safe to apply higher voltage to the output of a MIC2920A voltage regulator?
Surmises only - hard to be sure for a specific part with no hard data.

Connecting one as stated and measuring current flow into regulator would tell you something.

A look at the block diagram at the bottom of page 5 of the datasheet  suggests you will be trying to reverse bias junctions in  Q24 &amp; Q26 (top right of page).I'd expect the 4.5-3.3= 1.2V overvoltage to be low enough to have a good chance of being safe. 

Is power applied to the regulator during programming? If not you may breakdown internal intrinsic body diodes (which we may not have got). After which anything can happen. 

You mention a reverse protection diode. It's not obvious where you were going to put that. It's usual to place a diode from regulator output to regulator input - Schottky probably a good idea.