Not really. As I mentioned in my comment, it might make it easier, but not simpler.
For one, maintenance, probably becomes harder even. And it won't be "a docker image", but a docker-network (-compose, k8s or such) because running requires not just a single service, but a webserver (https), runners (async workers), redis, postgresql, elasticsearch, file-storage and so on. You'd need some 4 to 8 images all interconnected to run it.
And secondly, docker isn't omnipresent. I can't just copy a binary into /usr/bin , run it. I'll need docker, networking, docker-knowledge, logging, monitoring and so on.
More so: if a docker is a solution to the setup of complex piece of server-software, than certainly docker is a solution to the setup of a simple piece of server-software.