Because he most probably wouldn't know how 'bad' Slytherin is, so he wouldn't be thinking to himself "Not Slytherin not Slytherin!" thus resulting him being sorted in Slytherin. I don't think he'd fit in well with his peers there so he'd be alone.

If he didn't meet Ron then Harry would've probably shook Draco's hand and when Draco gets sorted into Slytherin he probably wouldn't think it was such a bad idea. But then over time he'd probably realize that he didn't like Draco's sort.

Harry met Draco before he met Ron - in the robe shop - and decided then that he didn't like him and, I think, even started to dislike Slytherin as well. He still would have said "not Slytherin" when he'd been sorted.

However, Ron was the first friend Harry had and was greatly important and loyal throughout the series. I don't think it would have effected which house he went into, but I think not being friends with Ron would have impacted things later on.

I strongly believe that Harry was and always will be a pure Gryffindor at heart. Maybe he had some Slytherin qualities, but no matter, I feel like he would have been in Gryffindor. Maybe his adventures wouldn't be the same if he never even spoke to Ron, and the war would be entirely different, but being in Gryffindor would totally stay the same.

He wouldn't know to ask not to be sorted into Slytherin without Ron, but once being there his gryffindor part would come to surface, because he wouldn't be able to do to people what Dudley and the Dursleys did to him for years and thus stay without friends. And we arrived to the importance of the Dursleys. Go Dursleys.

Even if he wouldn't have thought "Not Slytherin" in his head, there's no saying the sorting hat would sort him in Slytherin.