The short answer is yes you can. The long answer is two fold;
1 - Be sure to get a Nano with the header pins supplied separately and solder them in on what is usually the back side of the Nano. Check with orientation of the one supplied.
2 - When you program the Nano with the CEC software, the calibration parameters will not be saved. These are stored in the EEprom, not the flash memory. You will need to go through the CEC calibration procedure, which is different that the stock procedure. The CEC procedure goes back to the original way of using receive and zero beating a know signal. The BFO is the same, just remember that the value will be different due to the change in crystal filter.
Because of point 2, most get frustrated that the Nano reprogramming did not work. The significant thing is that the BFO is most likely off, and the receiver has very little sensitivity (it is aligned outside of the 11.0555 pass band - check for the exact frequency, I do not have it handy at the moment and the grey matter is getting old).
You can then swap between the two as long as you also change out the display.