Not the GP, but if I'm going to use make anyway, sure. init/systemd/upstart scripts for a system install, make run for a local install. It's exactly the same idea as running "node start" (apologies if I have the invocation wrong, I'm not really familiar with the node ecosystem).
A makefile is just a way to group commands together conveniently (at least, that's one aspect of it). So you can just type "make run-server" or whatever you want and it's just like running a script.
It's probably not something I would do on a production server, but it wouldn't hurt either.
It is also a way to write down and share very complicated command lines that you want to generate only one time because it is a pain to type it each time. So, a kind of self-documentation.