No, Facebook wouldn't allow it, and we wouldn't recommend it anyways. Facebook requires a 1 domain to 1 app relationship, and there's no way around that.
Beyond that, it's generally not recommended to have 2 domains pointing to the same content/site because:
* It hurts your SEO - You have 2 duplicate pages for your content, which means Google will give each 'half' the power that they'd get if they were the same.
* It's bad for social sharing - Again, 2 URLs will have 2 different Like counts, which means it will look like it's less popular.
* It's generally bad for branding, but that's up to you.
What we would recommend for 2 domains is setting up one to redirect to the other. That way, you can still post links to both domains, but the user will always end up at one unique domain.
I hope that helps answer your questions,
Alex
Using JFB connect with one FB app and multiple domains
