If a child stuck his finger in a toilet bowl that contained some toilet bowl cleaner and licked the finger, will the child experience poisoning?

I doubt that there is enough to cause a real problem. If the kid has trouble drinking fluids or eating it may be from a chemical burn on the tongue. If so an evaluation by his doc would be reasonable.

If this is his only exposure, I doubt that he would’ve come into contact with enough of the toilet bowl cleaner to cause a problem, although it is always possible to have a chemical burn. If he has any symptoms whatsoever, call poison control. Good luck.