It's possible, but not recommended. You'd be putting a lot extra stress on the dedicated server, and that'll amount to high latency for everyone. If you have a network and another computer that's usually idle, run your server on it. That's what I do. Otherwise just make a listen server.
Yes, you can run a dedicated server and play on it. Most people don't realize that you can connect to your internal ip address to play on your dedicated server from the same machine. To find your internal IP, go to Start > Run, then type "cmd" in the box (Without quotes) and the command prompt will pop up. In the cmd, type ipconfig, then it will find your internal ip address. Your internal IP address is the one under IP Address. Now start your dedicated server, then start the game your server is on. Open the console and type "Connect" followed by your internal IP.
What are you all talking about? I do this all the time. Just install the ded server. Run it. Go to "play esf" and go on your server. Make sure you make it the way you want. Or else it will say like "Half-Life" as the server name. I do this all the time. It doesn't create server lag at all. Then again, I have a fast computer. Maybe that's it.
You don't need to find your internal IP. At least I never had to.