Well besides the fact he would probably be kidnapped by enemies of Konoha, I'm not sure if he would gain respect. I mean he's still the Jinchuuriki of the demon that almost destroyed the village. Besides Gaara was the son of the Kazekage and even he was feared and shunned by the village - that happened even with the people knowing who his father was. So I wouldn't count on that.
Furthermore, if he got respect, maybe people would start to expect him to surpass his father, laying a big pressure on him, using the excuse that because he's Minato's son, he shouldn't have troubles exceeding in everything. As we know from the manga, he's always been crappy in chakra control. Maybe he would have taken his training a bit more serious if he knew from the beginning who his dad was, but that wouldn't take away that he sucks in some areas of the shinobi training. Then if he didn't show enough progress for other people's liking, they would have been disappointed in him and that would also hurt Naruto (having someone disappointed in you because you don't fulfill their requirements is not a nice feeling, I can assure you that)
But the last part of my answer is all just thinking of course. I don't know what would have really happened if he got a bit respect, but this seems like a plausible scenario to me ^^;
