EPiServer Mail will use the connection string configured in the EPiServer.Common configuration, by default the connection string named EPiServerCommon
If EPiServer Mail itself works with the new database I don't think there should be any issue with the bounce statistics web service specifically.
Is it possible to specify which database EPiServer Mail should use when registering bounce mails?
Quite some time ago an upgrade was made and the database was switched from EPiServerMail to one called EPiServerMail4. How does the Web service dealing with bounce mails know that EPiServerMail4 should be used insted of EPiServerMail?