It's certainly fine to use Perch just for that. It's as simple or as complex as you need it to be. Certainly for adding it into an existing static site it would be my choice.
However, there is an argument for using a third party service for the blog. She could use something like Tumblr to do blogging and just link to it in her menu. Another popular option is to post on Medium, as is Google+ (although I find that one impossible to use, personally). Still, I'm with those including Jeremy Keith who recommend keeping control of your content, rather than entrusting it to sites that can disappear overnight if they so choose. In a case like this, though, it's probably not a big deal.
I'm also wary of clients who want a blog because it's the done thing. You know they will forget about it in a few weeks or months, and nothing looks worse on a site than an inactive blog. So I try to convince such clients not to bother.