Yes, you can do what you are asking. You do not need a TV there, once you get it set up on your network, you will be able to control the cable box remotely via your slingbox. This may actually be preferable if you do not wish to interfere with your main TV entertainment when also connecting remotely.
Another option is to get a wireless bridge (sometimes referred to as a wireless gaming adapter) and connect it to your slingbox. If you but a 4 port bridge/gaming adapter you can also plug in any devices you have that have internet supported applications (TV, Blu-Ray, Roku, ETC).