IMHO, you want to stay as far away as you can from building a webpage in FW. It's a graphics editor and will do well for making PNGs or GIFs to import into an HTML file in DW, but you wouldn't use DW for image editing or creating graphics, so the reverse is true.
I've seen too many terrible results when people (especially those just starting out) try to create a page or even a whole site using a graphics editor to do the work of an HTML editor.
You wouldn't use a hammer to paint a wall, any more than you'd use a brush to hit a nail.
I'm sort of getting that impression ... that I should create single graphics in FW as needed and export them. But technically, is it possible to do what I'm contemplating, or am I just misunderstanding the functionality?
The functionality is there, just as a webpage can be built with Photoshop or InDesign (I think it can with InDesign).
The implementation is where the problem lies.
All to often PS or FW webpages are rendered nearly unvievable as they were originally meant to look because of browser differences, and worse yet, because they don't use HTML or XHTML elements the same way as a "traditional page" does, they are almost invisible to search engine robots.
Example: you build a page from a PSD and it's the entire page, with slices and hyperlinks mapped into sections of the slices.
A search bot reads the page as a picture. It may (or may not) even bother with indexing or even checking the links from the mapping, because the priority is set for HTML links, either in a nav bar, or a menu. More often than not, image maps are used for popups or other "same page" content, and they are overlooked to avoid redundacy.
Leave FW to the graphics.
Build your site in Dreamweaver, and ADD graphics to it. Don't build a graphic and try to make it function as a site.
FW and PShop are best used for design comps, slicing and optimizing images for the web.
Have a look at the following tutorials.
Taking a Fireworks (or Photoshop) comp to a CSS based layout in DW