You have left out information that is needed to see if this will work. First , it sounds like you have been using the 2 drives in another computer. Were they used in a Raid 0 configuration in that computer? Raid 0 is where the data is striped so it is necessary to have both drives to be able to use the data on the drives. If you had been using Raid 1 on the drive both drives would have the exact same data on them so you could just install one of the drives in your new computer to use the data on that drive.
So then, only if you had used the 2 drives in a Raid 0 configuration would you be able to use them in that drive enclosure. It states the configuration at that website.
Non-Configurable, JBOD: RAID 0 - Disk Spanning function
Installing the drives in that enclosure and not having them used in a Raid 0 config would probably cause you to lose all data on the drives, if you tried using them.
Personally, i cannot trust any mechanical device from experience, so i always put backups of any data i do not want to lose on CD's or DVD's. Yes, it would not matter to me if i had to use a 100 DVD's if the data was important enough for me.