Does a complete thought have only a verb?

A complete thought does have a verb; but having a verb does not make a group of Words a complete thought. A complete thought must have at least one verb, but a complete thought can also have several verbs.

An incomplete though that does have a verb is called a clause.

A group of Words becomes a sentence when it is a complete thought. Some examples:

The cookies that Mary made were passed out to the class. (The dependent clause 'that Mary made' has a subject and a verb, but it is an incomplete thought.)

I watched TV while Mary washed the dishes, packed the lunches, and made some coffee. (There are four verbs in the sentence, but the sentence is a single complete thought.)