Senjutsu training alone could produce interesting benefits for Naruto.
1.) I don't know that he'll learn Genjutsu, but he may become better at breaking it. Genjutsu is the opponent altering the flow of chakra to your brain. To disrupt it one needs to channel chakra away from their brain momentarily. If that fails you need an ally to do it for you.
When Naruto fought a 30% version of Itachi during the rescue Gaara arc he properly tried to disrupt the flow as Jiraiya taught him, but Itachi was too strong. The genjutsu was broken by Sakura/elder Chiyo placing their hands on his shoulder and channeling in their external chakra.
Now, with Senjutsu training Naruto may be able to break Genjutsu by channeling inward external environmental chakra.
2.) I'm fairly certain he'll be much faster, perhaps faster than mere training can produce. I don't know about Sasuke's forbidden jutsus.
3.) He has a couple of jutsus that are incomplete. The wind release shuriken rasengan and "That jutsu." I have a feeling those will be complete when he returns, assuming he finishes his training.
4.) The Kyuubi is supposedly a manifestation of evil chakra during bad times. Naruto may need external chakra to control the Kyuubi, but that's mere speculation.
5.) I would like him to learn more summoning techniques, primarily the frog stomach, and regular toads. Also, sealing techniques seem to involve the toads. Jiraiya and Minato were obviously excellent at this jutsu/s, so maybe Naruto will learn this.
6.) I don't know how dumb Naruto is in battle. He has certainly improved (Kakuzu fight), when even Kakashi is impressed. I believe it's abstract ideas that he has a harder time with. That's why he was a poor academy student and other training although he does learn jutsu's well.
Also, I always liked Gamakichi, and I'm glad he's starting to look like a badass. Maybe he'll get his father's Katana at some point. I'm probably wrong on over half of this.