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There is no listener you can use to see if the browser is being used. Sorry. Additionally, it is my understanding that you cannot even listen to the network connection to see which sites are being accessed through it.
If you think about this from a security standpoint, the BlackBerry wouldn't be a very secure device if an application could see this - someone could use the ability you're asking about for nefarious purposes.
Again, from all I know about the platform - there's no way to do this.
I believe you could write a background application that watches to see when the browser is the topmost screen on the stack, but I've never tried anything like this.
Actually, the way to do this is force all connnections to go through MDS (this is a BES Setting I believe) and parse the logs to see which sites are being accessed through the information MDS writes to the log about what it's doing. You will likely need to turn on a higher level of logging to be able to see which addresses are being accessed.
