Often is is possible. The range of the crystals signals' max swing are small. Where the XI pin needs to accept these small AC signal. Hence on the FUSE on the ATmega. Which also enables the XO as a Hard clamp to excite the crystal. The crystal dominates the voltage making it small. Additionally, it is important to have the proper parallel capacitance on both the input and output of the crystal. When the XO(0) is tied to the XI(1) along with the crystal and its parallel capacitor, noting that it is in the range of 10-40pf, the total parallel capacitance will be significantly increased. Where it may be possible to reduce the XO(0)'s parallel capacitor, if XI(1) does not add too much.
Anyone attempting this should really inspect the signal on an Oscilloscope to ensure the nature of the wave form is stable and stress its tolerances. Likely by changing the parallel capacitors to find the min and max's before failure. And varying VCC of both chips across is allowed ranges. As to determine the ranges is not unacceptable.
That said the datasheets refer to a version with a suffix T that have an CKO or Clock output on pin 1. That would be best and change the ATmega's FUSE for TTL input. Where Ignacio's answer is very valid and stable. Just the opposite direction.
I would point out that you will have the issue that 12MgHz is not a typically supported F_CPU speed in the code. I have toy'ed with changing the speed in the past, as to do just what you are attempting here, but with a different clock source. And found it requiring so many changes to the Arduino libraries, which are typically #IF'ed to either 8 or 16 so many places not using a nice formula, it was not worth its cost savings versus cost in maintenance. As a starter you may want to refer to SE: "Arduino at 11.0592MHz".