Absolutely. Perfect use case. This is exactly why you need Teiid.
1) Does all your databases have same schema? or are they separate?
2) Do you want to write reports based on this schema, or are you open to create a new view model?
Both are possible with Teiid. You can slice and dice the data any way you want with Teiid. Using Teiid Designer, you can import the schema from one or all of these sources and and create source model(s) and then you can create view model based on these source models to fit your reporting needs. At runtime, when you query your view model, it will gather the data from your sources and present in a consolidated view as you defined in your view model.
Then based on whether you are writing the reports in your application or using a BI tool, Teiid offers the either JDBC or ODBC access to get to your view data. There are plenty of documents/examples on the Teiid's website for your reference.
If you have any questions, please post to the discussion forms.