RAH, it's been my experience it all depends. GSH do have an advantage in that they reach a much larger size than most other minnow species, meaning that unlike say FHM for example, they get big enough to avoid predation by all but the largest of bass. This means, a few adults reach a "safe" size and can be your breeder stock. Sometimes too many get this size and can be a pain. I don't see that often though. I often see GSH being slowly removed from ponds over time, particularly ponds with little shallow water areas and steep banks. This combination produces few area for GSH to spawn and few areas for their young of year to take cover and feed. Usually, the first stocking produces a good number of fish who reach adulthood. These fish are stocked at the same time as or before LMB. Meaning they have a jump on the LMB and reach sizes too large for the initially stocked LMB to feed on. This original generation of GSH do well. However, as time goes on, poor spawning success and heavy predation on the young that are born leads to few if any new GSH reaching maturity. Over time as the original GSH die off from old age and with little or no recruitment, GSH eventually die out from the pond community.
GSH can prey on LMB eggs, but again this is generally a good thing as LMB tend to over reproduce which leads to stunting. I see no disadvantages to stocking GSH in a pond designed for growing bigger LMB. In ponds designed for growing trophy sunfish, I'd leave them out.
