Yes, you can -- Quartz Extreme is just Apple's name for offloading some of the graphics processing of the system to a supported video card. In essence, the video card will do a lot of the processing of the visuals in OS X so that your physical computer processor doesn't have to do it, making the OS X visual effects a bit faster.
Yes, you can have 10.2 without Quartz Extreme -- if you don't have a supported video card (any NVidia card or an AGP-based ATi Radeon card with at least 16MB of RAM) then you'll get plain-old Quartz. They won't look any different, but Quartz Extreme will be faster than Quartz.