Coordinate category base with posts page name?

I see a number of discussions here in the forum about removing the category base, but I don’t have a need for that. What I’m interested in is coordinating the category based with the posts page name. I.e.:

Under Reading Settings, I’d set Front page to display a static page. Then I’d set Posts page to a page called:

example.com/blog/

… so that a post might appear as example.com/blog/2008/10/post-name/

And then under Permalinks I’d change the Category base to “blog” as well, so that when I displayed Category archives, they’d appear as example.com/blog/category-name/ — i.e., they’d appear to be right under that blog page along with all the posts.

Would this work? Would it break the installation?