No. He did not pursue artistic pursuits. He had a nation to lead and he was more preoccupied with guiding people or worship of God. However, he did use literary devices such as vivid analogies and visual displays such as drawing in the sand to teach.. in other words, for productive and educational reasons.
Bukhari (6417): The Prophet (ﷺ) drew a square and then drew a line in the middle of it and let it extend outside the square and then drew several small lines attached to that central line, and said, "This is the human being, and this, (the square) in his lease of life, encircles him from all sides (or has encircled him), and this (line), which is outside (the square), is his hope, and these small lines are the calamities and troubles (which may befall him), and if one misses him, an-other will snap (i.e. overtake) him, and if the other misses him, a third will snap (i.e. overtake) him."
That said, do we see him in the presence of some "artistic displays" at times? Yes.
- Visual: He watched with Aisha as the Abyssinians did their "dance" i.e, display with weapons.
- Literary: He listened to 'good poetry' such as the poetry of Umayya b. Abu Salt. He also encouraged Hassan ibn Thabit in his use of poetry to defend him/Islam.
- Architectural: Construction of Mosques; architecture falls into the category of arts.
Prophet Muhammad (ﷺ) had the greatest understanding of the world and what is to come. Such that if any of us knew, we would literally "laugh little and weep much" per his words. It would be hard to just 'enjoy life' knowing what is to come. Logically, a person with that awareness would not be spending most of their time for anything other than productive and beneficial reasons.
I hope this answer helps and sets up the context, somewhat.