Nginx conf for a SaaS - is there a decent way to handle this scenario?

Question

I'm developing a web app. Users will sign up and will be assigned a sub-domain which will allow them to access content via account-456.myappsdomain.com. The intention of having that sub-domain though isn't for them to visit it directly. Instead, they'll be informed to point the CNAME for www.their-own-site.com to account-456.myappsdomain.com in order for them to be able to visit their own domain and view their content directly on their own domain. Is is possible, using Nginx, to create a configuration that will allow this without me having to edit the config or add a virtual host every time a user signs up for an account?

Currently, my app uses the host header (splitting on the dots to get the account-456 bit) to get the account ID, and then sets up the theme based on that. I assume that with this new sort of configuration, I'd check the host header for their domain (which I will have had them enter into the app), query for the domain (and the account it belongs to) and set up their theme that way. Is this correct?