As long as the traffic server knows about the closure, it will definitely work you around those. What you see and what it does may depend upon the nature of the closure. If it's a planned closure, then it will begin the route by working around it. If the closure comes up unexpectedly (e.g., an accident) then the traffic problem alone is enough to start the device working a different solution, even before any 'official' closure occurs. The 6250 will check traffic conditions along your route and in a significant radius of your current position every 2 minutes.
The Professional 6250 is a pretty nice piece of kit. You can load up the specs for your vehicle and it will manage routing based upon weight, height, etc. It has it's own cellular hardware, so it gets all of the necessary traffic data without need for any other hardware. The only gripe we've heard is with regard to tunnel codes for hazardous goods. That;'s been requested for quite some time, but hasn't appeared yet. For some logistics companies, that can be an issue.