If I read all the poetry ever written (i.e. was extensively "trained") and then, using a statistical analysis of all that material, synthesized some syntactically-correct stanzas, based on (and following the rules included in) a request I received from someone else (and if I did this only when asked, not say when I fell in love or saw a sunset) and using only words from what I had read, would I be "writing poetry"?

Let's not lose our damn minds, m'kay?