Yes.
You need 4. (At least, with any setup I've seen.) However, you could use 4 partitions, instead of 4 drives. Have one side of the mirror use RAID 0 on two partitions on two 1TB drives. The other side of the mirror could use RAID 0 on two partitions on one 2TB drive. Ought to work.
I don't offhand know how much you'll get of the usual speed benefit of using 2 drives like what RAID 0 often brings. (Actually, I'm rather certain it's implementation-specific. So it might work pretty well, or not.) But 1 drive of 2TB is likely to be a bit slower than 2 drives of 1 TB each, because the single 2TB drive may require reading from a different part of the drive, instead of having two drives reading/writing different spots simultaneously (since they are separate drives).
Is this the best way to do it? Maybe not. (Maybe Server Fault may be a better site for asking such a speed/performance-related question.) However, regarding the question of whether such a thing is doable, I would say, certainly. Just tell the RAID software to work with partitions (rather than drives).