To an IVA - Yes providing your insurance will allow it.
Unregistered car to MOT thats not an MOT (even if the garage don't record it...is it still an MOT? - Might need to provide proof of MOT which they can't do because no registration) - minefield.
Risk vs Reward.
All it takes is one police officer on a bad day interpreting the law differently and your car is crushed for being untaxed, uninsured, unregistered and you find yourself a hefty fine and points.
Personally, I'd do the IVA test driving there - if you don't have confidence in your build....will the IVA tester? After than, worst case, you need a retest - £90 still? Then you can book an appointment at the local garage to rectify emissions if needed and be covered. Yes it costs more, but if you've already sunk £10k into the build, whats an extra £100-200 for legal peace of mind?