To answer the questions directly, yes, you can have a TV tuner card in your server.
However, the reason Alvin Smith directed you to Direct TV and the Slingbox is because installing the TV Tuner in the server is one thing but being able to watch the TV video on the other pc's and you HTPC is another this altogether.
Installing the TV Tuner card in your server will, for the most part, only allow you to watch TV on the server; unless you use a device or software that streams media to other computers.
Along withe Slingbox, I recommend checking out the ATI TV Tuners and the ATI Multmedia Center. It's been a couple of years since I've used an ATI TV Tuner or the MMC, but I do remember it having media streaming functionality. If I remember correctly, it required one computer to act as a "media server" and installing a client on the other computers.