The tomato is a tropical perennial plant, period! I live in Malta, EU now. For the zone, imagine Arizona surrounded by ocean. Desert with rain from September to May.

For the first year the indeterminate tomato plant has immature, spiked foilage and produces fruit. From the second year on it has different leaves. Rounder and in clumps. Almost looking like a plant growing up in the air. From this we get vine tomato fruits all year round.

For the tomato plant the lack of frost, overall temperatures and daylight hours appear critical. Bringing into a greenhouse in a Northern climate would not address the daylight hours and the winter would see no fruits. However, it is possible to save the plants this way. When I lived in the UK I used to do this with tub tomatoes and woth lobelia, (another perennial grown as an annual).

I say give it a go. If it's green, plant a cutting. If it has seeds in it, sow them. I have grown carnation plants from wedding button hole flowers and hundreds of melon and cucumbers from supermarket fruits