I recently learned that SQL Server 2012/SSIS 2012 has a feature called the Integration Service Dashboard. Does this feature include row counts? If not, is there an efficient way to modify it to supposed row counts?
Using the basic level of logging in the catalog, I've found that custom logging using a script task returns OnInformation messages contining the custom log entries in the standard execution reports. Within the script task, use Dts.Events.FireInformation. There's an example in the help region. You could capture your row counts this way.