Yes. Many do. It's no problem during high season.
There is every chance you will join up with other hikers on the same route.
Be sure to bring an emergency whistle if you do hike solo. You can alert help quickly if you sprain an ankle. Never side trip alone.
Be aware, however, that Park policy is not to allow hikers to register alone for safety reasons. You may need to sign in with someone else in line. (In 2004, when we paid our park fee, single hikers were not questioned.)