"I eat and she eats."
Translation:Ithim agus itheann sí.
Give that PIE was SOV rather than SVO or VSO, your conclusion lies on shaky grounds.
It is generally agreed that Hellenic (giving rise to modern Greek) was one of the earliest to diverge from PIE, and that Italic (giving rise to Latin and all of the Romance languages) diverged shortly before the Celtic languages did. The Germanic languages are relative latecomers.
You don't use itheann for "I eat". The 1st person pronoun is included in ithim.
Ithim - "I eat"
Itheann tú - "You eat"
Itheann sé - "He eats"
Itheann sí - "She eats"
Ithimid - "We eat"
Itheann sibh - "You guys eat"
Itheann siad - "They eat"
Itheann Pól - "Paul eats"
Itheann an fear - "The man eats"