Yes and this is one way to do it. Create a customization for the BAQ Report parameter screen. You then create the necessary code to capture a value change for your filter fields and then update the dataView (using a field that is not used. Once this is done you will see the value in the ReportParams field (as shown below). If you would like I can provide a working code sample that will lay it out better.
edvReportParam.dataView[edvReportParam.Row]["Character01"] = myFilterField.Value;