Never bag if you have a choice. If you get behind enough to get "hay" rows, and you can't spread them out, either by double cutting or blowing them, then picking them up is better than "smothering". We catch the clippings on the greens. We spread those few clippings back out in the taller grass areas. Even our tees and fairways, maintained at .500" for HOC can be mowed often enough to let the clippings fall. On rare occasions, we have to drag to knock down clippings. For "spring cleanup", I had them run the sweeper behind all the rough. 90%+ of what was picked up was brown, dormant matter that, while good insulation, slows green up. All of that is being worked into my new compost piles. I hope to have them in a top dresser and back where they came from by August or September. I wouldn't be afraid of the clippings from a synthetic yard. I might be tempted to compost them separately, just to make SURE, but there should not be anything in the green leaf tissues to worry about. The one time of year I really like mulching mowers, is fall, BUT you can get the same results when grinding leaves with a rotary by making multiple passes. Just don't windrow it all in the same direction and then try to grind. If your mower will side discharge, throw the debris back and forth until it disappears. I like to show my crew how to make concentric "figure 8's" and reverse the direction for the next time.