It seems that conversion from cdt to ai is possible using CorelDRAW and represents creating a AI Adobe Illustrator graphics from CDT template based on predefined settings. This is because CorelDRAW can also produce graphics in Adobe Illustrator forma (.ai). It is unlikely any other program would be capable of handling .cdt templates for this purpose, which means no other options how to achieve cdt to ai conversion exists.
Open CDT file Open AI file
A set of applications used by professional graphic designers
Desktop publishing software