You could run Wordpress today, afaik. Anything that can run in a Docker container can run on on Convox. You'd just need to use some sort of hosted database service like Amazon RDS to persist your data.

edit: Just looked at Wordpress a little closer. I didn't realize it expects a persistent filesystem, which I guess is what you're asking about. Convox follows the 12factor.net philosophy of ephemeral filesystems, so you'd need to figure out a way to persist files to S3 or similar...

Stateful?

https://github.com/roots/bedrock