It certainly 'can' be done, but you'd need to decide on whether you want to run MQTTSubscribe as a driver or as an extension to add info from some other driver.
Part of the fun is learning how to build your own images, but you can avoid even that if you have it mount directories on your host.
Try a google search for 'weewx docker' and check out the results. One base image I'm aware of is
https://hub.docker.com/r/mitct02/weewx which has sources at
https://github.com/tomdotorg/docker-weewx although the documentation there lags the current image version perhaps a little. If you look in the Dockerfile there you can see how he adds things to his image by downloading a lot of well known extensions and skins and installing them within the image. You could add a couple lines there to add MQTTSubscribe pretty easily or better yet create a derived image of your own that is based on the author's starting point.
Give it a try. Should be very doable.