Most Epson printers will stop printing if cartridges are empty. But my Epson 895 has an option to print Black only, but my Epson R200 doesn't have that option. So I guess the later the printer the less options you have. The RX600 appears to be an MFD which probably won't print if you have empty cartridges. Your printer takes the same cartridges as my R200 click here
for good value compatible cartridges.