I love the hate Konohamaru gets despite being a 2nd Naruto. Also he knows naruto's sexy jutsu and upgraded it with his shadow clones when he made harem no jutsu.
But to the question it all depends on his animal contract I think. We've only seen sage mode based on two summoning contract animals and Hashirama's which who knows where he got his sage mode from maybe he has a slug contract like Tsunade. But Konohamaru being a Sarutobi is more likely to enter a summoning contract with the 3rd's monkeys. Until Kishi elaborates more on Sage modes, Konohamaru will probably not get one, unless he ends up signing a summoning contract with the frogs at Mt. Myoboku like naruto did and even then it's not a guarantee. I think it'd be neat if everyone with an animal contract had the chance to achieve a Sage title for that animal(Obviously only if they are good enough, even Jiraiya didn't have full frog sage mode like naruto did)