Using tmux to host a server
What you want can be done. I've seen it done with GNU screen when Tmux wasn't around yet. However, I would not consider it good style to do it.

There are better ways to do this. Daemons are simply "normal" processes being run in a particular way. That particular way usually means to fork "twice" (so that the parent/child relationship gets broken) and plugging stdout, stdin and stderr to some file (or /dev/null if no logging is desired).

There are tools aplenty out there to achieve what you want while also ensuring that there is a policy in place if the process unexpectedly goes down. After all a service should be available as close to 100% of the time as possible.

Read up on:


daemontools
supervisor
daemonize
runit


Arguably your system will already have one of these or a very similar tool installed. But you don't give enough information for me to provide more detail.