The over voltage might explain the increased leakage but you're be very unlucky if you destroy the PIC. It will be able to withstand 6.5V and the diode will drop some voltage, even at low currents. Perhaps if it's operating at its maximum temperature rating, whilst being subjected to the absolute maximum voltage, then there's a real risk of damage, otherwise it's highly unlikely.
Maybe we are reading different datasheets, but the one in front of me(*) says +5.5V on the Vdd pin respect to the Vss pin is the
absolute maximum rating.
And in my experience, exceeding datasheet absolute maximum ratings, often even slightly, have the tendency to blow the parts up very quickly, or worse, do some sneaky damage that will cause undefined, hard to debug behavior later on.
Maybe this particular part is different for one reason or another, I don't know, but extraordinary claims require extraordinary evidence, and without such evidence, I would not speak about blowing it up would be
unlikely.
In any case, trusting the prior experience on particular PIC parts surviving and working properly even after severely exceeding absolute maximum ratings is a stupid engineering decision, since the manufacturing process for the parts can change at any point of time without prior notice. This is especially dangerous advice for a noob, since noobs will have enough strange issues to solve in the vast world of MCUs already; overvoltage damage is easy to avoid by not applying overvoltage on purpose.
Get the power supply within specs with ample margin, decouple with a lossy electrolytic, and apply proper ceramic decoupling right next to the MCU power pins, take basic ESD precautions, and you can expect that any strange behavior is most likely due to bugs in
code.
(*)
http://ww1.microchip.com/downloads/en/DeviceDoc/39605F.pdf