Yes I installed the software on a virtual machine which is on 24/7 with all the songs. (Doing this since 2005)
There is also a cloud solution from SAM, but that comes with very limited basic website. It is also possible to do a combination with Sam Broadcaster and SAM cloud. If you need to turn off your PC, you can make sure that SAM Cloud will handle the rest (except the website part). SAM Cloud has also limited storage. You can always upgrade your storage to store your songs.
So if you need a website with a request system, you need Sam Broadcaster Pro running on a Windows machine. And the website can be run on the same machine or on a webhosting site which uses PHP and MySQL (or any other SAM supported DBMS).