If you set to ATA, some SATA specific things will not work. So if you use an SSD as well, TRIM will stop to work for example. If you change this setting, it will definitely hurt your SSD in long run.
Another problem may arise if your OS on the HDD/SSD is strictly configured to boot from an AHCI device.
For example, you installed Windows 7 in AHCI mode, and later set this ATA-compatibility mode, Windows won’t boot, but gives BSOD bcause of “inaccessible boot device”.
However, there’s not much risk in changing this setting just to see if you can boot from the ODD afterwards? You can safely change it, and evaluate if that setting had any effect regarding ODD boot capability. Just remember to turn it back for everyday use, especially if you use SSD in you system.
That’s quite self explanatory 
I’d try to change this first, before you start to play with the AHCI/ATA game.