hap: I'm sure that's been done many times. you can't directly dump it (easily) but visually dumping it is no problem. I did this for the noritake VFD displays with HD44780 interface but it was a work project. I just took the documentation and manually banged in the bits into a text file and wrote a program to convert it back into a binary.
Once I got an HD44780 LCD from a copy machine, which had a really strange font ROM in it. Unfortunately I am not sure if I still have the chip; I removed it and put a "Standard" chip on the LCD, and I am not sure if I saved the old one. from what I recall, it had "buttons" made up of ROM characters, like boxes with text in them which showed up next to keys on the display. Display was 40 by 2 line one.