Speed dial numbers are always stored in the CM database, and they are saved in the DMA output tar file to be used for upgrade. DMA backs up both CM database and directory data.
Fast dials are user data, and they are stored in the directory in 4.x. In 7.x, the fast dials are stored in the CM database. This is backup as part of the directory data backup.
Directory does an export for "Fast Dial" entry while migrating from 4.x to 7.x; you can see the entries for the same in the csv file