RAID 5 requires 3 drives to operate, so it sounds like a drive is not working or not connected, in which case, adding a third 2TB drive will not do anything for storage capacity, but will instead reintroduce redundancy and bring speeds back up to what they should be.
This process should be completely automatic, or may require you to log into the NAS and tell it to rebuild the array. You will not have to migrate data during this process, however, the NAS may become very slow for a number of hours or days (for 4TB it should take a few hours), while it rebuilds the array. Storage capacity will not change, as stated above, unless you add another 2TB, i.e. running 4 in total.