My question is just as mentioned in the title of this post: Would you call an infinitive verb a true verb?
I can't find any direct mention of it anywhere on the web. The CMoS (2010) catalogs Infinitives under Verbs and defines it as follows:
An infinitive verb, also called the verb's root or stem, is a verb that in its principal uninflected form may be preceded by to {to dance} {to dive}.
However, chompchomp.com mentions this about infinitive verbs:
An infinitive will almost always begin with to followed by the simple form of the verb, like this:
To + Verb = Infinitive
Important Note: Because an infinitive is not a verb, you cannot add s, es, ed, or ing to the end. Ever!