If one were ever stopped by law enforcement, I would suggest they "politely" comment that they thought the sign was meant for cars and hopefully get off with a warning. Technically though, it could apply to all motors. I think one needs to look at the sign's original intent.
A short portion of my daily commute involves the Pearl Harbor Bike Path, which is the only "scenic" bike path we have on the island of O'ahu. It has a few good viewing spots but it primarily runs behind retail stores and through unkept wasteland used for petroleum pipeline access. About midway on the Path there is a sign stating "No motorized vehicles". The sign is not at the trailhead where you would expect it, so that would be my defense IF I were ever cited riding an ebike (hoping to purchase one in the coming weeks).
Now, the sign was put there before ebikes appeared on the radar. It's purpose was to warn moped riders, motorcycles and cars. Believe it or not, I've seen all three on this Path at one time or another. Due to the fact that the government entity in charge of the Path won't replace the broken stanchion at the trailhead, the homeless were able to drive their vehicles on the Path and park next to their illegal campsites in plain view. Local law enforcement didn't do anything about it then, so I seriously doubt they would stop a cyclist who was actively pedaling his ebike. The only time law enforcement did any "enforcing" on the Path was when pedestrians started complaining about mopeds buzzing up and down nearly running them over. For a day or two, moped riders were cited and then law enforcement headed back to the donut shop.
If the trail or path you're looking to ride on with your ebike is monitored by a group of individuals looking to blame ebike riders for their troubles in life, you probably won't have a prayer. Otherwise, it's your call. Ride responsibly, and if you ever get cited look for a new place to ride.