Yes, and other NSTs in the country incorporate motorized use (for example, the Continental Divide Trail) on federal lands. On non-federal lands, corresponding land managers make decisions about use and policies, including motorized use. In Alaska, another national trail - the Iditarod National Historic Trail - allows motorized use.
The Frequently Asked Questions on the BLM site for the feasibility study specifically address the motorized use:
Q: How are motorized uses managed on national scenic trails?
A: While Section 7(c) of the National Trails System Act (Act) states that "the use of motor vehicles along any national scenic trail shall be prohibited," Section 7(j) allows vehicles to be permitted on certain trails. These may include, but need not be limited to, snowmobiles, motorcycles, bicycles, four-wheel drive or all-terrain offroad vehicles, and trail access for handicapped individuals. The feasibility study will examine the appropriateness of motorized trail use along the trail. If Congress designates the Alaska Long Trail as a national scenic trail, they can specify acceptable uses as they did with the Continental Divide National Scenic Trail, which permits the use of motorized vehicles on designated segments of the Continental Divide National Scenic Trail. Where allowed, the Act intends for motorized use to occur in accordance with regulations prescribed by the appropriate Secretary in accordance with other Federal laws, or any State or local laws.
Q: What types of uses could be allowed on a national scenic trail?
A: Potential trail uses allowed on designated components of the national trails system may include, but are not limited to, the following: bicycling, cross-country skiing, day hiking, equestrian activities, jogging or similar fitness activities, trail biking, overnight and long-distance backpacking, snowmobiling, and surface water and underwater activities.
While National Scenic Trails are primarily non-motorized on federal lands, section 7(c) of the National Trails System Act lists several exceptions to this and gives a significant amount of latitude to local land managers and the administering agency for determining what use policies are appropriate for which trail sections. This practice can be seen in other National Scenic Trails, for example the Continental Divide Trail: about 23% of the nearly 3,100 miles of the CDT are multi-use trail systems that include motorized use. Every time a new national trail is added to the system, the NTS Act gets amended with specific language about that trail. The Continental Divide NST is written in the Act with specific permissions for motorized use along the trail. Nothing precludes the Alaska Long Trail to be written into the Act with a similar language.