The advantage, imo, of using a non-WordPress theme is that when you start building the actual product, you're using the exact same files. As far as I know, if you get a WordPress theme, you'll have to scratch it when you start building your actual site. Am I wrong about this?
You won't have to start over when building your actual site if you build/use a WordPress theme. At my dayjob we build most of our client sites in WordPress so my starting framework is in WP (it's basically a combination of HTML5 Boilerplate + Blueprint + Starkers).
When I need to build a non-WP site or convert a WP site to HTML/CSS, I go to my framework WordPress site, view the source and save it as index.html.
There's only a few things that need to be changed, like the path to the stylesheet and images.
Bonus points: you don't have to be an engineer to do it, so if you have a business guy, he can go be useful for a change. (I kid, I kid.)
If you want to make your application match your Wordpress theme (not sure if that is necessarily a good idea), you can do it fairly easily. In Rails, you'd View Source on your homepage, copy/paste everything into layouts/application.rhtml, delete the chunk that renders the main content on the page and replace it with <%= yield %>, and you're ready to go for development purposes. (You'll eventually hack it to bits for SEO, collapsing Javascripts/CSS, and other reasons, but you'd do that with a HTML/CSS template anyhow.)
One more question. You wrote: "If you want to make your application match your Wordpress theme (not sure if that is necessarily a good idea)".
Now, say I want to put up an MVP of some application, which is just a landing page. Shouldn't I include some kind of screenshot of what the application will look like?
If so, what design do you use for screenshots of the application itself? Do you use the same theme? A completely different design?
My MVP used a cheap ThemeForest theme for the Rails part which shows minimal functionality, but the hero shot image is a racially ambiguous caryoon character, showing the successful businesswoman busy killing it because she was smart and bought my service. It is downright frightening to the engineer in me how radically that increased the number of requests for info I got from ladies. The marketer in me has to soul crush him some days.
This point stolen shamelessly from slide 9 of my Business of Software 2010 talk on selling software to women. I spent all day today on it today (well, when not breaking into Diaspora).
Then, to rebuild the backend template, one can do a 'curl' and then post-process using a script. So when the BizPeople change the layout, one can regenerate the backend template immediately.
It's on GitHub : contributions (of code) welcome.
In a second phase, you can go back and do it from scratch, when you have more time and resources.
Wordpress allows you to decouple the "info site" stack from the web app stack, which are not necessarily the same technologies - and so this can go way beyond just MVP.