As long as you've done things right at your end then it should work fine. We have had customers who have done the same kind of thing in the past with our other theme, ClassiPress before the .csv importer was implemented (i.e. they had an existing Classifieds site they wanted to migrate data over to ClassiPress and imported the ads from the database side).. This kind of thing is ultimately outside the scope of what we officially support, but if you've got the ability to do this then there's no reason why it shouldn't work.
The Eva child theme is not a product created by AppThemes, so you can communicate directly with the developer on the Marketplace page for the product
here in the comments section if you wish, however there does appear to be a recent comment regarding responsiveness. Thanks.