Not in all states/localities... Virginia clasifies "Motorcycles" as any vehicle w/three or less wheels...
§ 46.2-100. Definitions "Motorcycle" means every motor vehicle designed to travel on not more than three wheels in contact with the ground and is capable of traveling at speeds in excess of 35 miles per hour. The term "motorcycle" does not include any "electric personal assistive mobility device," "electric power-assisted bicycle," "farm tractor," "golf cart," "moped," "motorized skateboard or foot-scooter," "utility vehicle" or "wheelchair or wheelchair conveyance" as defined in this section.

Ride Safe,
Fired00d

I guess the motorcycle definition can be looked at in two different ways.
First from a motorcycle standpoint, I would agree with that definition.
But from a car standpoint that is manufactured and sold new, a "car" could have three wheels as well. There is a history of 3-wheeled cars thoughout US cruising years. There have been some eco cars designed with 3-wheels and they have been considered cars. They're making them in the UK now, or at least within the past few years.
So a motorcycle is three wheels or less and a car could be considered three wheels or more. In my mind just having three wheels does not automatically push it into the "motorcycle" class. My thinking would be the intent of the vehicle, but not the number of wheels. If the Morgan had four wheels it would not be any more safe or unsafe than with only three. So a helmet in that case would "seem" to be not needed as this in my opinion is a car, not a motorcycle. I know, put my money where my mouth is. We're among friends and I'm just rambling for now.

I tend to stretch things a bit out of the box, so maybe I'm way too far outside the box on this question.
I've always thought that making a Morgan style 3-wheeler would not be that difficult to pull off. Look at the body work, a lot of flat side sheeting. But if I were to make a 3-wheel car, I'm not sure what requirements are needed.
I've been into streetrods for many years and a gearhead in general all my life. I know people that have built scratch cars and got them plated and in my case I bought a chassis and body and built the rest myself. So I'm thinking that "if" I wanted to build a 3-wheel car, I could and have it plated as a car. My mind is now running 100 mph and I'm thinking all these thoughts... That's when I get dangerous. That's when my wife kicks my ass and tells me to shut my mouth when I'm talking to her.

But come on, how hard would it be to make a similar car to a Morgan?