Grammaticalization of third person singular -s
Almost certainly not. The usual 3rd person singular inflection in Old English was -th or -eth and it looks as if its replacement by -s came about by a process of sound change.
I will promote my comment to an answer here too.
PIE -ti -> PGmc -di/-ði -> AS -t/-ð/-þ -> ME -th (Southern)/ -s (Northern) -> ModE -s
The Northern -s came from the influence of Norse mediopassive -sk; eventually the Northern usage became standard in Modern English. According to this, the form has been inflectional at least back to late PIE.