The answer appears to be that it is possible:
http://codex.wordpress.org/Creating_a_Static_Front_Page
Configuration of front-page.php
If it exists, the front-page.php template file is used on the site’s
front page regardless of whether ‘Settings > Reading ->Front page
displays’ is set to “A static page” or “Your latest posts,” the Theme
will need to account for both options, so that the site front page
will display either a static page or the blog posts index. There are a
few methods to do so.
As for the blog page, I think you can find what you’re looking for here:
http://codex.wordpress.org/Page_Templates
Specialized Page Template
Create a template for one Page: For more extensive changes, intended
for just one specific Page, you can create a specialized template
file, named with that Page’s slug or ID:page-{slug}.php page-{ID}.php
In that specialized/custom template file, use the get_posts() function (http://developer.wordpress.org/reference/functions/get_posts/) and other similar functions to get and list the posts.
You can use the add_posts_page() function (http://developer.wordpress.org/reference/functions/add_posts_page/) to add the page to the menu.
So, in your front-page.php, you’ll have a reference to a static page that you create in your code. You’ll then also create a second page for your blog page using the specialized page template.
I’d be curious to know if there’s an easier, more straight-forward way to do this.