In short, yes... you would have a problem with RAID6 and using a smaller drive. RAID6 itself has no way to dynamically re-size the RAID to a smaller disk. You must either:
- have a RAID controller capable of dynamically resizing the RAID volume
- copy your data elsewhere, and completely rebuild the RAID and then restore the data back to the volume.
I have only ever seen one RAID card that could do dynamic resizing, but it did not support RAID6. I doubt yours would either. Also, even with RAID5... there was a HUGE hit on performance while the raid was resizing.
Copying your data elsewhere is also a big risk, due to the fact that you're taking your redundant array... and moving the data to a non-redundant storage. (even if it is temporary)
At the end of the day... just buy another 2tb hard drive. They're not terribly expensive... and trying to avoid it will just give you much higher risk of data-loss.
In the future... you might want to look at other RAID alternatives that do support that sort of functionality. ZFS can... as well as a few other proprietary RAID appliances (DroboFS, etc...) allow you to use mis-matched drives for redundancy. I honestly would not recommend anything but ZFS for this sort of thing.