I’ve recently seen Paulownia planted in the open in the Hoyt arboretum, Portland, OR. Both were struggling, with half of the foliage dead (as were some of the legumes). By contrast, if you look on YouTube for the WeGrow operation in Germany, you’ll their Paulownia seedlings (I think they actually plant out in Spain) reach tree size in under a year (!).
It probably depends on the climate you can offer whether it’s worth trying or not.