Indeed, if you use Sign-on Meraki Authentication then the user data is maintained in the Meraki cloud, not what you want.
If you just want the users to enter some data (name, e-mail, phone number, etc.) and store that in a MySQL database, use a custom captive portal with the click-through method.
If you want them to actually login, use the login method. But then you'll also need a RADIUS server with the known users that syncs with your MySQL database each time a new user is created.
I must've misunderstood your last question, and I'm still not sure I do. If your question is whether you can experiment with this without actually having a Meraki hardware device, no it's not possible to do that. But you can participate in a Meraki webinar and get one for free or request a Meraki trial. If you're a Cisco partner and you have access to dCloud, you can explore a demo dashboard there.