Funnily enough, it might have. We’ve seen that the Night Elves are willing to make deals for logging rights, and the Warsong didn’t seem to have any problem working with the Darkspear, or the Goblins in Ashenvale. In fact, all the outbursts of violence Grom had were in relation to either his hatred for humans, or when he was already besieged by the Night Elves. If Grom was willing to work to work alongside the Darkspear, and willing to honor a deal with the Goblins, whose to say the Night Elves (who we have many examples of allowing logging when asked) wouldn’t allow the Warsong?
Hell, the Warsong were there gathering lumber because they were going to construct the settlement that Thrall wanted. Had they known the supposedly empty forest was actually full of Elves, giant sentient trees, and had a literal demi-god protecting them, whose to say he would attempt conquest, when Thrall had been explicitly taken them to Kalimdor to avoid conflict.
Do we? We don’t have much to go on about Grom after the second war up to the events of Warcraft 3. What we do know is that he spent fifteen years living in the wilds of Lordaeron, hiding from humans, eking out a living. After being inspired by Thrall, he worked alongside Thrall and Ogrim to rescue the Orcs from the internment camps. When Ogrim fell, he accepted Thrall as Warchief, and was happy to follow Thrall to Kalimdor.
Thrall : “Grom, are you alright?”
Grom Hellscream : “I’m fine, little brother. Luckily, they only injured my pride.”
Thrall : “Great, 'cause we’re getting out of here now. We’re leaving the human lands for good.”
Grom Hellscream : “Finally. Follow me. I have an idea.”
From the sounds of it, Grom hated the humans and wished to have nothing to do with them. Given he spent the last fifteen years in constant conflict, followed Thrall who went to Kalimdor explicitly to avoid conflict, and attacked the humans because of his long history and hatred for them, a diplomatic attempt from the Night Elves doesn’t sound doomed to failure to me.