I'm looking for a way to hide a facet on the server-side at runtime/dynamically. Can this be done?
I am not entirely sure what you want to do but Facets are, like everything else, an element of the DOM.
Let me know how it goes.
If you bought the Enterprise edition of Coveo for Sitecore, you can use the layout personalization feature of Sitecore on the Coveo for Sitecore Facet components to define conditions where your facet should be hidden (see Personalizing Coveo Components).