I can't see him enter the tournament. As you said, they're really hammering home the plot point that the MC is less a hammer and more a scalpel. In the back. Less Luna and more.... calculating. Putting himself in (or simply participating by being forced) would ruin all that because certainly it seems even the MC knows his main strength is being under estimated. If you bring home the gold, no one's gonna wanna go up against you.
Agree about MC but, just a thought, entering the tournament is not the same as winning it.
The tournament probably wouldn't have been mentioned, if it wasn't going to be featured & MC entering is plausible under a few circumstances.
Could be as simple as Luna wants a chaperone.
Perhaps, when we get promoted, Cordia or Wilfred may choose to send us. Perhaps Wilfred sees it as a way for MC to recognise his physical abilities, as well as his plotting & scheming skills.
Either way, he's probably going to get "grumpy" & have a complaint about it.

Also, where you say "if you bring home the gold, no-one's going to want to go against you", I'm not sure about that.
Maybe MC would quite enjoy not having anyone want to go against him?
Also, don't forget that being champion quite often puts a bigger target on your back and you may find that more people want to go against you.
IDK, but I don't think the Frenetico would have been mentioned as simply a throw away comment.
I fully expect it to feature in the game.
If it features in the game, MC will surely be there.