I never buy an adjustable fstop lens. (meaning one that changes fstop as you move the focal length).
Why not?
Go out and try to shoot street photo with your current lens (kit?). You'll quickly find out, that ideal lightning conditions are quite rare and you can't tell your subjects to wait a little longer for better conditions or move, so they will stand in direct sunlight and you can finally get usable shutter speed.
To sum it up - no, I wouldn't buy 18-105. It's a slow kit lens and a much better option would be to get 24-70 2.8 which I've mentioned earlier. Yes, it's quite expensive, but will you be happy with blurred images or missed focuses, just because your lens wasn't fast enough? Street photography is about your reactions, capturing the decisive moment. If you can't capture it RIGHT NOW, the moment will perish. Have that in mind when you decide what to buy...
If you're just an enthusiast, who wants to travel and take some snapshots, you'll be fine even with a compact camera. If not, I wouldn't waste money on lenses you'll need to replace soon, just because you wasn't patient enough and didn't get more money.