Sway bar settings generally do not have an impact on how "stiff" your ride quality is, per say. That is usually directly impacted by spring rates and shock valving (mostly high speed in compression), etc.
Stiffening up the sway bars generally only effects the side to side transfer of weight more commonly referred to as body roll.
So yes, you absolutely can run your sway bars at the stiffest setting for the street, (I prefer it and do it all the time). The only likely adverse effects you may have by doing this is less grip on wet roads and the car having more of a tendency to want to follow the grooves in the roads a little more.