Both, actually. AM stations that currently employ hybrid digital have the digital part overlayed onto the analog signal. It extends into the adjacent channels which is why you hear a digital hash when you tune 10Khz off of the station. This all-digital mode fits in the existing channel but there's no analog component. Most existing tuners were designed to tune hybrid or full-digital on either band.
The FCC would have to approve a station's transition to all-digital. The question is.. will any DO it. There might now be enough car HD Radio penetration to make it viable with the right format and clear promotion. There are enough cluster-owned "underperforming" AMs that someone might give it a shot. Let's say you own five stations in a market and one of them is an AM at 1570 carrying a simulcast of an FM just to keep it on the air.. it might be worth trying something cheap and easy just to see. Certainly can't hurt as there are a lot of AMs not generating enough income to pay the electric bill.
The big question is the format and I'm sure that'll vary by market. Gotta be a niche, localized format that'll appeal to mobile listeners. Would probably need to have a streaming component as well for those without HD Radios interested in the content.
For example, in Detroit, I'd chase the Middle Eastern community. It's a sizable population unserved by local radio. Lots of businesses and other organizations to buy ads. Could sell value-added ads to English-speaking businesses, as well. Wouldn't take much to get the community involved in programming and staffing it. Yes, that COULD be done with existing analog AM, but music simply sounds terrible on AM, anymore. The public has come to expect at least MP3 quality with music. This'd deliver it.