I think the immediate serious risks you are referring to would be an allergic reaction which, as far as I understood, would be evident during the infusion. You'll be watched during that time. I had a negative reaction (serum sickness) to remicade a few weeks after the first infusion. Fever, rash, horrible joint pain. It cleared over a few days with Benedryl and Tylenol. I didn't continue on the drug. I tried Humira later and had a very severe reaction. Again, a few weeks after the first dose. They are referring to it as 'lupus like syndrome' but also included some nerve damage which isn't usually part of the lupus like reaction apparently. The symptoms cleared (in the hospital) within a week or so except the nerve damage which, although has improved, continues 10 months later.
These reactions are seemingly very very rare though. It seems the vast majority of people find the biologics to be a godsend. I wish you the very best and would be interested to hear how it goes for you.