Rather than relying on hearsay from "internet experts", just go and look for yourself firsthand.

The Mega board we have uses an AMS1117 as the 5V regulator.
Here is the datasheet for that regulator:
http://www.advanced-monolithic.com/pdf/ds1117.pdf

Maximum input voltage is shown near the top of page 2. 15V DC.

If you instead use a Genuine Arduino branded Mega board, the specs for that board are available from Arduino here:
https://store.arduino.cc/arduino-mega-2560-rev3

Scroll about midway down, and click on "TECH SPECS".
It will show you Input Voltage (limit) 6-20V.

So all good on that front.
But do read it yourself, rather than accepting as truth what other armchair engineers might claim.

And if you are worried about "spikes" beyond the rating of the regulator, it is pretty simple to just put a zener diode across the input (12V to GND) to provide spike regulation to whatever value you select. Eg. a 14V Zener will limit the spikes to 14V or less.