I say maybe. Of course it depends on the positions that each hold w/in the company. If you are both normal worker bees, it's one thing. But if one is a manager it can get hairy. I've dated a guy that I still work with to this day - he's our IT guy at the office. I must admit that it was super weird when we first split and we totally avoided each other. My PC was all hosed up and I left it alone because I didn't want to call him for help! But, we got past it all and have ended up to be good friends and are fine at work and don't even give it a 2nd thought anymore. We didn't have a bad break-up or anything, though. Some people knew we were dating, and others didn't.
When I used to work part time at restaurants and stuff you see co-workers date all the time. Different sort of atmosphere I suppose.