The reason your custom attribute is not imported may be that you didn't write an upgrade script creating the attribute. EcomDev_PHPUnit doesn't copy the database but runs the normal Magento scripts.
When PHPUnit is started the EcomDev extensions kicks in with
EcomDev_PHPUnit_Test_Listener::startTestSuite(). This method invokes
EcomDev_PHPUnit_Model_App::applyTestScope() and this one calls
EcomDev_PHPUnit_Model_App::initTest() launches the normal install/upgrade script process by executing
This means you can either
- write upgrade scripts for attributes,
- use fixtures or
- copy the database.
As far as I know (I'm still new to EcomDev_PHPUnit myself) your options for EAV attributes are number 1 and 3.
I didn't try copying the database yet but it should work. I'd go with option 1. Writing upgrade scripts for attribute sets, groups and attributes can be much work but it is a best practice and there is a high probability it will pay off in multiple ways (less manual setup for other projects / working copies, better transparency, ...). This nifty script by Alan Storm may be of help.