Can I AnalogRead an AnalogWrite pin on another Arduino board?

I want to transfer an analog value 0-255 from a Nano to a Mega (without using serial). Will AnalogRead read a PWM output properly?

No.

You may be able to come up with something that uses the pulseIn() function.

Nano supports software serial on all pins. Mega has 4 serial ports. Why not take advantage of that?