Are cat probiotics only good for their digestion?

...or can they help with other things too, i.e. allergy relief, shinier coat, etc.?

Probiotics also boost the immune system in that improved digestive health leads to a healthier cat and a stronger immune system. With a stronger immune system they can resist infections easier.

 In terms of allergy relief or improving the appearance of the cat's coat, I'm not aware of a connection but then again, I'm not an expert in probiotics. It would seem reasonable that a healthier cat would have a shinier coat, though.

Makes sense.  One thing probably affects the other in this case.  Thanks.