When using an Alternate Host instead of the source or target Exchange server there are no statistics.
Source and target servers are configured to allow statistics collection and it is visible, that agents do write the information to the emwstat.dat file. However the Statistics Agent doesn't attempt to collect the statistics from the Alternate Host, EMWSCA.log doesn't mention the Alternate Host and when the Statistics node is highlighted in QMM Exch in left side pane then in right side window it is visible, that the server which is using the Alternate Host is not being processed by Statistics Collection Agent at all.
Developers confirmed this to be a known issue with Statistics Collection Agent when using an Alternate Host and an official Change Request ST70654 has been created and the issue was resoved in Hotfix 20100709EX
To resolve the issue please refer to SOL65450 and Hotfix 20100709EX.
To resolve manually:
Use the SQL Enterprise Manager or any SQL administration tool which allows to modify the content of the DB.
Important: create a back up of the SQL DB first.
Stop the Statistics Collection Agent.
In QMM Exch DB find the table named "SERVER".
Open this table and find the entry for the Alternate Host server, copy the ID for this server (it will be the very first column, the value could be a 2 or 3 digits value). Close the table.
Find the table named EXCHSERVEROPTIONS and in this table create a new row with the ID of the Alternate Host server (just create new row with this ID and nothing else). New row can be created/inserted at the bottom, under all existing rows. Close the table.
In QMM Exch data find the server which is using the Alternate Host, right mouse click on this server and select Refresh.
Reapplying Agent Configuration (committing changes) is also a good idea, but not absolutely necessary.
Start the Statistics Collection Agent and ensure the server in the right side window is processed (this might take a minute or two, depending on the environment), when this happens statistics should be visible when using the Statistics tab.