First of all, do you know for sure that you can fly to IAD if you are ticketed to BWI? Some fares may not qualify for this change, especially those that were competing with a fare sale to BWI (i.e., Southwest) but not to IAD.

If they allow you to fly to IAD on your ticket and seats are available for purchase on all legs at the time you check in, they should definitely give you boarding passes for all flights at the time you check in for the first leg. Obviously if any leg is sold out at the time you check in, they will not be able to issue a boarding pass for that leg. If that is the case, you'll need to be assured they will guarantee that you get to your destination even if it means the next day. I'm not so sure they are required to do so.

What you are planning to do seems rather risky to me unless they will issue boarding passes on all segments at the time you check in. Remember, if a PHL-PIT or a PIT-IAD flight gets cancelled while you're en route from SFO to PHL and you don't already have all of your boarding passes, the backup of ticketed passengers could cause you to get stuck in PHL or PIT.