The short answer is yes, but understand that all non essential services are suspended and you enter at your own risk. I ventured out this morning to a local National Park unit and saw the usual amount of folks hiking and walking their dogs. What was different was some parking was closed and no access to Visitor Centers or NPS employees. More critically, no access to indoor plumbing.
To make a visit to a National Park successful and enjoyable during this difficult time, it is critical that visitors step up and are considerate to other guests and clean up after themselves. Actually that would be nice even when the government is back up and running.
I think at the campgrounds especially that visitors need to be prepared for an adjustment. Even if you have a reservation, the campsites are likely to be more of a first come, first serve proposition. Not to mention that you may need to be prepared to pack out all garbage and waste as trash cans are likely to be full.
However, if you are quick on your feet and able to rough it a little, then you may find lesser crowds than normal which could be a benefit. Take care. rk