Unfortunately not, the index table is not designed to store relations of custom fields, only the words.
With the regular engine it might be possible with some major modifications, but I’m not sure about that either. You could maybe try adding the following code to line 607 (should be an empty line) in file wp-content\plugins\ajax-search-pro\includes\classes\search\class-asp-search-cpt.php
It should look like this after editing: https://i.imgur.com/itX1Lc1.png
Just change the “author_field_name” and the “fulltext_field_name” to the custom field names.
Please not that I have not tried this code! So be careful.