How to display a widget on a page with no theme?

You should read this. It’s completely possible, but you have to go through the right process. First you should register a new “sidebar” and call it whatever you want to call that page you want the widget to display on. Then you need to call that sidebar into the page’s template file, after which you can add and remove widgets from your dashboard.

This all hinges on you having access to the code, if you don’t I am afraid the answer is probably not.

If you can alter the code, then all you have to do what I said above, and create a new page using the page template you created.