No, they won't. Relationships don't fall from the sky, you have to actively do something. If you are good looking you might be hit on by those with courage of making a move, but keep in mind that is also further restrained by the places you go to. For example hardly anyone, even with great game, would approach you in a library.
I use that phrase very loosely, but I'll rephrase to help articulate what I meant.
Essentially what I am saying is rather than focusing one's effort into solely seeking a partner or companionship, one can divide their efforts into bettering themselves and their interests in life which helps subsequent social encounters bloom into friendship and potentially more. Though it is merely my opinion that over emphasizing pursuit in others can shroud motives, intentions and behavior in others and one's self.
But again, this is merely a perspective and opinion, so take what I say with a grian of salt. Especially since I've been single for over 3 years now lol.