I doubt anyone on board would feel it. It’s all relative. They’d be traveling at such a high rate that falling into and then out of the gravity well around Earth would be like your driver-side front tire clunking into a pot hole.
I guess I’m thinking of Centripetal force but I’m not sure you would feel that either without a physical connection to the orbital center.
I’ve read a lot of Robert Forward who wrote extensively on tether assisted maneuvering which creates a physical connection leading to a felt force.