I would hope they designed it where you can keep riding. It seems possible. Pick some charge level (say 20%) and provide less and less power assist as you approach that. Once you hit 20%, a control system tries to keep it about 20% charged. Basically you enter a mode where the battery becomes a buffer (between the pedal and wheels) rather than a power source. The bike would feel sluggish, but it wouldn't stop working.
My reasoning that it's probably doable was based on efficiency.
What is the end-to-end efficiency of the generator, electronics, and motor combination? If it's 75% efficient, then you need to pedal 33% harder than normal[1]. If it's 66% efficient, then you pedal 50% harder.
Unfortunately, I can't find real data, so those efficiency numbers are guesstimates. Electric motors and generators can be very efficient, and I would hope that they'd use efficient ones for an application like an ebike.
As a point of reference, pumped hydro can be 70-80% efficient[2], and that involves a motor, a generator, and mechanical losses. That's not an apples to apples comparison, though.
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[1] Where normal means a 100%-efficient link between pedals and wheel. Actual bike chains aren't, but they appear to be 95% or more.
"rather hard" is really underselling things. Without considering generator->motor losses, 250W is a lot of power, even for a larger (>80kg/176lbs) rider. For basically anyone who doesn't train on the bike, this is an unsustainable effort.
Even a floor of 100W would rule out smaller/less athletic riders.
And once you are up to speed, you coast. Even on a normal bike. With the battery as a buffer, the ebike could easily bump you up to speed and use 250W or more for just a little while and then 0W for stretches.
