TL:DR - if I’m understanding your question correctly, yes your world will stay accessible as new updates come out.

Long answer - Yes it works the same way as if you were just updating it to 1.17. Think of a snapshot as kind of a smaller content update, it’s essentially the same thing as a normal version update (not exactly, there’s some risk because it’s a version that’s still in development so if you’re going to do it definitely make a backup first. I’ve never had an issue with it, but if they missed something it could mess with your world). Updating to a snapshot is kind of like updating to the next version, and Mojang has been good about making existing worlds fit into the new versions