My 06 Octavia vRS passed the NCT last month without any washer fluid! And I doubt the rear wiper is a requirement, as most saloon cars don't even have a rear wiper. All that matters I think is the front wipers. So 99% chance you'll pass.
As for actually getting it fixed, obviously check there's washer fluid first, check if you can hear the pump motor working (but you said this is working on another car), then spray for it for a few seconds and look under the car to see if there's any fluid spilling out anywhere. Could be one of the fluid tubes come lose or something.
Unfortunately I can't help you more than that, I also need to get the rear sprayer fixed on mine. Yes, the Octavia has a rear wiper, despite being shaped like a saloon.
Good luck
