First - the adapter pictured will let you use a SATA drive in a system that only supports ATA, and not an ATA drive in a SATA system, which is what would be needed.
Second - this unit has no internal cables, so you would need an adapter with the connectors in just the right location for them to line up.
And last - there is very little space to spare in the unit - so even if you did find an adapter, I doubt that you could get everything in.