I don't think calibre-server.exe itself should change to be a service, since calibre is cross-platform. However I do run calibre-server.exe as a service using
NSSM (I used to use srvany.exe, but that's old and dead) and it works great. The only thing I changed from default was to run the service as my normal user, so that I didn't have to mess about with setting permissions to files for network service account (using local system won't work if you want to have network access). I just have to remember to manually stop it before upgrading so that calibre's install doesn't force me to reboot.