... If you try to run an ATmega328P at 16 MHz and 3.3V it probably just will not work (or not work reliably). My calculations say the maximum frequency at 3.3V is 13.3 MHz.
I run an Uno/328 on 3.3V at 16MHz everyday without any troubles.
I am still not clear though what happens to the crystal / frequency as you reduce the voltage