Check this website for park by park information. www.nps.gov/.../index.htm The information can change daily and not sure if website keeps up. I was in Yosemite in 2013 when they shut down. They did not allow in new visitors, park programs were cancelled and roads were closed. We staying in the park and were given a few days to vacate the park before the lodge closed. Again every federal shutdown and park is different. I was on a 7 National Park tour and ended up going home and trying again the following year. Road Scholar did provide transportation to airport for return home. I hold my breath every year as my goal is National Parks. Shut downs have become so common it is always in the back of my mind when choosing dates.
Guessing hard for RS to keep you posted as it changes daily and NP's could be up and running by then. Very hard decision on both sides of the coin.