Hi Matt,
I wrote a PowerBuilder application that does almost exactly what you describe (Mafia Manager), however it was accomplished using the web browser OLE object that you do not want to use. I may have misunderstood and you DO not mind using the OLE object as long as you can fire PB code from actions within the OLE object and the answer is, yes you can and it isn't too difficult.
You can fire PB code based on actions in the web page being hosted in the OLE object using the InternetData function, which exists in a descendant of the InternetResult class and is called automatically by the context when the user does something (e.g. clicks a url) in the current web page.
Look at InternetResult and Inet classes, and the GetUrl and InternetData functions to get you on the right track. If I remember right there are other events/functions that you can use to determine what the current URL is and what action was taken. IF you need me to dig up my code from that program send me an email and I'll do it.
Hope this helps.
Rich Bianco
PowerBuilder, .NET Blog