In the next generation, there can be a lot of variation among the seedlings depending on how these genes reshuffle in each offspring. You may get a few unique individual seedlings, or you may not. If you have the space and time to experiment, it's up to you. I've sown seeds from hybrid geranium and the number of desirable seedlings from those that germinate is low, 25% or less....but that's geranium, and a particular geranium, your experience could be different.

Depending on what it is, you may end up with something very similar to the F1. I'm no expert in this by any means, but I've saved a few seeds here and there from produce and from F1 plants. It doesn't hurt to grow them out and see what you get. I tried growing out F2 pepper seeds a few years ago and I kept getting 3 different types of peppers. Of the 3, the ones I really liked were seedless, so unless I took cuttings, I could never keep growing those. I've saved seed from white marigolds and they would never germinate. I've read that tomatoes grown from Campari F2 seeds are just like or very close to the F1. It is fun to try...I usually have some kind of experimental planting each season, but on a very small scale..

I purchased a honey dew from SAM club. It was golden yellow with green stripes. I never tasted a sweet perfumed honey Dew like that for a ling time. I saved the seeds and planted them. I was able to produce 25 of the same honey Dew. If it was not for the Ants and Squirrels I could have double crop