Plagiarism. Noun.
An act or instance of using or closely imitating the language and thoughts of another author without authorization and the representation of that author’s work as one’s own, as by not crediting the original author.
I would say no. If you or I did it, then yes. However, since a (presumably unaware) monkey is doing it via random processing, then it would be (IMHO) akin to an independent composition.
The Wolf