If I write values to the atmega's EEPROM, can I read them after I have reprogrammed the chip..
Yes, it will be retained also after you upload a new sketch when using the standard Arduino IDE configuration.
The Arduino bootloader (in its most recent incarnation) can alter/program EEPROM, but will only do so if you manually start the uploader (avrdude) and instruct it to do so.
If you upload a new sketch through an external programmer (e.g. AVR ISP, STK500 etc.), the default behavior however is to erase the chip (flash and eeprom) prior to programming. There is however a fuse setting available (on the ATmega's) that can be enabled so that EEPROM is preserved through the erase cycle.