Of course it is compatible, you mess up protocol and interface.
The correct question would be if the controller is compatible to the ATA interface specification. And the answer is yes.
So software like the CD-ROM driver can also run ATAPI protocol over the ATA interface.
Just make sure the HDD is really ATA compatible and not just AT.
Also the jumpers have to be set correctly, usually it is for the HDD: MASTER/SLAVE present and for the CD-ROM SLAVE.
HDD must be at the end of the cable and CD-ROM on the connector in between.
Problems may occur when jumpered wrong, like HDD to MASTER only and CD-ROM to slave or when jumpered to Cable Select when one device does not support CS.