I can't see how it could do any harm....
Many foods are naturally probiotic (promote good gut bacteria) and many are naturally antibiotic eg garlic. As long as you buy good quality ones and check what other ingredients are added in - obviously you don't want ones with a load of junk chucked in on top.
You may get some sort of "die off" reaction as bad stuff is killed off by the good I suppose, but that wouldn't be "harm" because of that I'd start slowly and build up gradually.
We do probiotics... 80% of immunity is in the gut. Probiotics are going to do far more to help an immune system than a vaccine imho (we do still vaccinate though) my LO is rarely sick, and when he is, he bounces back very quick. He can be around sick kids/people and not pick up their bugs fairly easily. Today... he's just had a reaction to something he's eaten for lunch...but he's in less than an hour appearing to have the reaction fade and his usual chirpy self. He had a fever several weeks ago...not sure why, it lasted overnight and by the morning he was done and ok again. He could just be naturally robust, but I've never seen a kid bounce back as fast as he does, an illness has never gone on for more than 24 hrs for him other than one mild cough about 5 months old that was over in a week.
If you're worried perhaps you could start with more probiotic foods before using powder/capsules...
Hope this helps