Yes, until they are OVERWRITTEN.
When you delete a file on a HDD, you do not delete the data. You just modify the Pointers in the File allocation table (FAT) to tell the operating system that it can "reuse" the sectors. Untill windows writes new data to these sectors the orginal data is still there.
That said, Are you reusing this drive in the new computer as a Operating system drive? If so you should do a re-install of your operating system and this will over write much of the data, and if the partition is redone and a new file allocation table is created, you probably are NOT going to recover previousely deleted files.
Deleted files do not get transferred, however you might be able to recover the deleted files as long as you haven't written data over the HDD. Try downloading recuva and see if you can recover anything.