Yes it's possible to recover data from a formatted hard drive specially if you didn't put new files/folders on the drive after the format.
I don't know if Recuva is able to recover files on a situation like that, the program is free so you can try the most important part is not to write anything to the HDD, you need to recover the files to a different drive.
I'm not familiar with hdata recovery, it seems the program can scan for the files and show a preview to evaluate if it can recover your files after purchase. Most commercial recovery programs will work that way, only do recovery after buying the program. In some of them is possible to save the search for data done by the program, this will speedup the recovery process because the next time you only need to load the search already saved.