You can if you are smart enough to load a server OS on the phone. To this day after running servers since I was 14 years old, I have never ever came across someone who actually run a full HTTP server on a mobile phone.
BlackBerry use Java, but you may be able to load an OS of your choice. You will be probably the first person to do so as far as I know(I could be wrong)
NOTE: I also don't think that you will get much support here since most of us are not programmers nor coders. (I do programming for fun, not for a real job or anything like that)