Question:

Can I make my native Fireworks/Dreamweaver popup menus persist using the Persistent Layer Pro extension?

Answer:

No, that's not possible. To be able to make a layer persistent, the layer has to be on the page (with a unique ID) when the Persistent Layer Pro behavior is applied to the page (at designtime).
FW/DW popup menus however, are generated through JavaScript at runtime in the user's browser. And as such, they are not available on the page at designtime to be manipulated by Dreamweaver behaviors.