How flexible or granular is the Process Monitoring feature? Can it be configured to, for instance, report on the failure of a file transfer? What data would it use for that?
More than likely, not for that particular situation. Essentially, once you enable process monitoring in Profiler, you wait for a collect cycle to complete. Once it does you will have a listing of currently running processes in that same configuration window, and you can then select which ones to monitor.
The reason why I say no is because I don't know if you can 'catch' it in time. Depending if it shows up, you might be better off trying to monitor the event logs and alerting on that.