The ability for your predators to control gizzards will depend more on the size of the top predator than on the number. Gizzard shad max out at 22". SMB eat fish that are 1/4 to 1/3 thier body length. So after a fish gets over 8" a 24" smb will probably leave it alone. SMB might eat fish up to 1/2 thier body lenght (like a LMB) but that would be the exception and not the rule. Even assuming they did a 24" bass would only eat a 12" gizzard. Long story short, SMB are not going to touch the gizzard shad population. I wish they could, smb that ate gizzards would grow huge!
My question is how big and how many gizzard shad can a walleye eat? Walleye can grow bigger than SMB and should be adept at feeding on open water fish like shad. I read one paper that found walleye in an oklahoma resevior ate gizzard shad and drum and put on most of thier weight in the fall.