If each of the drives is a 2TB model, then you will have a RAID 1. That's a mirror, in which case you will be able to do as you intend.
If OTOH the drives are 1TB models, then the data will be "striped" between both drives, in which case your proposed approach will not work. Instead you would need to reassemble the RAID.
You could possibly clone each of your drives externally, and then reinstall them inside the Lacie enclosure. To this end I would use a tool such as ddrescue.