Hardening off involves not only the temperature, but also and primarily the degree of radiation from the sun. Yours will probably harden off faster than those started indoors, but I think that the glass in greenhouses also diminishes the amount of radiation the plants receive indoors.

If I were in your shoes, I would harden them off for a few days in filtered light outside. I had almost as many pots are you have so I know the anguish of moving them all.

Fortunately, I think we are over the risk of frost here in Southern Ontario, but I will still be watching with care.

John