I know they are bad for the environment. Destruction of habitat. Waste of water which requires energy. Does this help or hurt the CO2 levels overall?
Well, golfers walk or use golf carts. And then there's *some* carbon sequestering from the grass and trees. But along with the water I suspect there are chemicals (fertilizer, insecticide) being used and running off into the ground water. And they probably also cut the grass quite often using a gas powered riding mower. My guess is the overall balance would be negative. I don't play golf, so if they go away, I wouldn't mind that much. I don't follow professional sports, so all of the stadiums and sports arenas built of concrete in the middle of a sea of concrete parking lots can all go away too.
The LEED for New Construction Reference Guide indicates that well-maintained turf is not environmentally friendly. They recommend limiting the amount of turf cover and using indigenous grasses and ground cover allowed to grow naturally. If I can accurately piece multiple sources of information together, I would consider the very short root systems of turf compared to other ground covers. Longer roots hold the ground better, aerate better and provide better habitats for underground critters. The lawn mowers used to cut the vast quantity of turf are probably not emissions controlled. If chemicals are used, there's runoff potential. And burritos mentioned the habitat for above-ground critters that must be destroyed.
Big negative, esp in arid areas (where they seem to proliferate). The water use alone is bad enough. The massive amount of runoff is the other big one. The one positive is that in some areas golf courses introduce trees (on the prairie, for example), which is kinda nice. Of course, there was a reason why there weren't any trees there to begin with...