Oh! Ethernet! Heck yeah, that library's going to require a TON of RAM. No way to do the 32x32 matrix and Ethernet together on an Uno.
As for the Arduino Mega...I do seem to recall some users getting the matrix working, but whether or not this can also work with the Ethernet shield, I'm not sure. There may be pin conflicts, or there may be timing issues of trying to handle network access and driving the display simultaneously. For pin selection, here's the relevant comments from the RGBmatrixPanel library source:
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// Arduino Mega hasn't actually been tested -- use at your own peril!
// Because digital pins 2-7 don't map to a contiguous port register,
// the Mega will require connecting the matrix data lines to different
// pins. Ports A, C, and L all offer the requisite contiguous 6 bits.
// I wanted to use PORTL in order to keep the external memory interface
// free, but accessing the upper PORT registers in assembly seems to
// require some additional flaming hoops and doesn't work with the
// inline code here. PORTA is used instead (Mega pins 22-29, though
// only 24-29 are actually connected to the LED matrix). Clock may be
// any pin on PORTB -- on the Mega, this CAN'T be pins 8 or 9 (these
// are on PORTH), thus the wiring will need to be slightly different
// than the tutorial's explanation on the Uno, etc. Pins 10-13 are all
// fair game for the clock, as are pins 50-53.
#define DATAPORT PORTA
#define DATADIR DDRA
#define SCLKPORT PORTB