The phrasing is not incorrect, but I think as a query for directions it's a little vague. The person you're asking does not know what you're after -- are you trying to get to a specific location, or asking if this street/road goes to a general area, or just trying to get some general information on where it goes without a specific goal of your own in mind?
So you could say "Can I get to X by going on this road?", or "Will this road get me to X?" (or "...lead me to X?").
As to street or road (as brought up in a comment), in the US we tend to regard a 'street' as a paved roadway that is in a city or town, could be a "downtown area" with lots of streets and buildings, or could be a suburban area with lots of residence driveways on the street. 'Road' usually means a paved roadway that is going to continue for a longer distance. But this isn't a strong distinction, the terms are used pretty much interchangably and will certainly both be understood.