There have been cases of people wiring up a 328P to a solderless breadboard with a 16Mhz crystal but with no padding capacitors and having it work fine.
There is some small of input pin capacitance for the clock pins (which adds to the external padding capacitance) and the biggest effect is most likely that the 16MHz will be off frequency by a amount then it would otherwise be without the 'offending cap', assuming the crystal/oscillator starts to begin with.
On the mega2560 board the 16 MHz crystal and padding caps are for the 32U2 USB serial converter chip, not the avr mega2560 chip which uses a ceramic resonator with internal padding caps. So as long as your PC recognizes the board when you plug it in
and you can upload sketches, I wouldn't worry about it too much. But Like Bob my guess is the cap is the wrong value and preventing the crystal/oscillator from starting up.
Lefty