Not by module, but you can get this information by object. For UBE's, there is a Last Execution Date field on the batch version table.
For applications, you can turn on Object Tracking, and then look at the results in the object tracking tables and/or reports.
That is right. And be careful turning it on in PD. Sometimes it can get in the way of other processes/kernels (I know it used to cause issues with package deployments).
I think they fixed that post a tools upgrade where it would caused kernels to go nuts - but I do recommend excluding certain apps everyone runs (and like UDC search and select stuff.)