Scott,
Hi. Unfortunatly this cannot be done with the current version. This does sound like an interesting feature request though, possibly a 'Create cookie called XXXX after form submission' and so forth but on the page where you are showing the gallery you would have to also look for that cookie and this type of implementation would either require customization to DNN etc... Simply put even if Dynamic Forms could create the cookie you would have to setup something to enforce that on the page outside of Dynamic Forms etc...
Dynamic Forms does have a few things you could do...
You could 'Display message to user after form submission' so therefore maybe have a hidden link that is displayed to the user once they submit the form or simply have the form redirected to the page you would like them to after form submission. This could be a page that is not included in the menu but is available to all users.
Another option would be to implement 'Only allow user to submit form one time' and then there is a message to the user which you can define such as (thanks, you already submitted this so to continue to the page click this link etc...). This is almost a 'survey mode' but it would come close to what you are wanting.
Finally... another option would be to use Dynamic Forms and auto create the userID so that they are being created without knowing it. You could have it create the user based on their email address and auto create the password for them... At the point they are redirected to the 'secured page' they are actually signed in as a user and if they ever want to go back to it they can simply check their email for their sign on information.
Hope you find these helpful, please give us your feedback if you end up using a solution and want to share your thoughts on it.
-Chad