Once accidentally powered a PIC24 with a 5.0V LDO instead of the (correct) 3.3V version...
The programming interface worked fine, but USB wouldn't enumerate correctly.
Possibly, analog functions, like the USB's PLL clock generator, weren't working. Over-voltage causes current to diffuse throughout the IC -- perhaps analogous to how your own brain feels woozy when it's running a fever! Digital logic can usually deal with an environment like that, but analog stuff, forget about it.
The amount of current flowing was fairly small, under 200mA. Nothing was getting particularly hot (including the LDO, because the whole board was powered from 5V in the first place).
Note that this was a current-limited case: the 5V LDO (supplied by 5V) was in dropout, so chewed up a bit of voltage itself. Even if the MCU had failed shorted, it wouldn't draw more than an amp.
I don't think you're guaranteed magic smoke, but doing it 1. from an unlimited-current supply, and 2. to a chip with a lot of analog functions in it (i.e., oscillator, ADC, radio), I don't see it working very well.
3.3V LDOs are cheap and plentiful. Use one!
Tim