Yes. Since pretty early on, and more strongly for a few years.
“eat” is an infinitive functioning as a noun which is the object of “will”.
Infinitives, gerunds and participles are words based on verbs which function as nouns or modifiers. They are called “nonfinite verbs” but they can’t do the job of a regular (“finite”) verb. Nonfinite verbs are one of the harder grammar topics.