Philip,
Yes! You must make sure that the geoprocessing service has the message level turned on to info so you will see all of the messages and not just errors and warnings. I believe this is "none" by default.
I then made a simple modification to the geoprocessing widget.js onJobComplete section to display messages. This was just to prove it was possible, but I am sure with a bit more effort, a new function could be added to display it the way you'd like. Here is a snippet of the modification that I made to the onJobComplete function.
//onJobComplete is invoked even if jobStatus is STATUS_FAILED.
//It hides this.infoNode so user can not see the error message!
//if(jobInfo.jobInfo.jobStatus !== JobInfo.STATUS_SUCCEEDED){
this._createErrorMessages(jobInfo.jobInfo.messages);
//return;
//}
I just commented out the if statement so that all messages would be displayed.
Regards,
Tom