Hi Mark,
No, the seeds do not have to fall from the vine. Once they are plump and look good for picking, you can pick them. I did ferment them when I saved seed. It looked like that should be done and so that's what I did. It worked good, lol. One fruit would be difficult to ferment, but since you know you can pick them from the vine, I suppose, you'll use more.
Remy

Remy,

Thanks--I've been waiting for a number of fruits to fall, so I should have a good supply. I'm going to end up with quite a few seeds, though. A check of one fruit suggests about 70 seeds.

I think one might be able to get by with only one fruit if, say, the flesh from another cucumber (seeds removed, of course) is added to bring the volume way up. Of course it would be good to cut down on all those chunks that might be hard to separate. I think this can be done by pressing the added flesh through a sieve or something like that.