The long answer:
Yes, it is possible but not quite the way you think.
Even though BlackBerry has no IR,
You can use a web-based or email-based remote control system -- and use your BlackBerry to remotely control the web-powered/email-powered remote control connected to a computer server (i.e. a plugin for Windows Media Center, etc).
Basically a gateway that converts web/email based operations to infrared commands. I've seen web-browser based touchscreen remote controls connect over WiFi to a remote computer that does the actual infrared hard work.
It is more work but it makes it possible for any wireless Internet device to control a home theater or home automation. Look up software such as MainLobby, Girder, myHTPC, Meedio (google these up) -- some of them include email/web plugins. You need devices such as a USB-UIRT infrared transceiver connected to the computer, and the USB-UIRT needs to be pointed to your home theater, and that computer needs to be connected to the Internet as a server. More help at "Home Theater Computers" at
www.avsforum.com/avs-vb
A BlackBerry user successfully controlled his TV using this manner.