I've got a second roof on the garage/workshop -
tin roof | insulation | tin roof
The new one has some sort of anti-condensation coating too, but that was really unnecessary as it's not the lower one!
It works well.
At a guess, I'd say it won't be a fraction as effective without the insulation. Can you use 2x4 instead, or even rip them to 2x1 (minus the kerf)? You ought to be able to find something that works at 4". Worst case, if the area is small, can you use Kingspan or similar (comes in a choice of sheet thickness).
I say 'small area' because it's expensive. Mine's done with metal 'rafters' and roll insulation between (4" thickness). It's made a big difference to the condensation problem, and it's now usable in the height of summer, too. but as I haven't been able to insulate the concrete walls or the up'n'over, it's not a complete solution.
I think it's worth the effort for comfort, but as Myfordman says, try to find something that will work in the space.