Why would you want to do that? If it's just so the terminal window isn't up, I would suggest using screen -> http://www.gnu.org/software/screen, or if using a mac you could run an apple script which would run the process silently:
do shell script "cd /Users/thaddeus/arc;
/Users/thaddeus/scheme422/bin/mzscheme -f loadscript.scm"
> how to run it alongside apache, or listening on a particular ip address?,
I think this is more an apache discussion point so I would suggest google searching 'mod proxy'. There's are tonnes of write ups on this kind of stuff and Linode.com has in-depth how to's. Mod Proxy just redirects incoming requests from an IP/domain to a specific port. As for Arc see the function (asv) which you can change the port number and just run it - I think it's in srv.arc.
> It runs well, so far so good, but I have the interactive interpreter. As soon as I shut down, the service disappears.
This is where 'screen' comes in handy. Screen is a threaded model: it assigns a single thread for each 'screen' used. It also has a built in command to detach from your screen session (CNTRL+a d). After detaching you can then close the terminal window and arc will still be running as a silent thread. To get back just launch screen with the option to re-attach ($ screen -x).