Can a probiotic like florastor select immunity boost help reduce your chances of catching a stomach bug at all?

Maybe/not. Probiotics are just seed cultures of germs that ae known to "play nice" in the gut. If they establish a major presence in the gut they can crowd out germs and yeast that are sometimes linked with gut problems. They are useful during or after a course of antibiotics that may kill off well behaved germs in the gut. Otherwise their use may or may not be beneficial in the long term.

Controlled trials have not shown "probiotics" to be useful. These do not boost immunity. Some of the "probiotics" may cause side effects from D-lactic acidosis.