Will Suckers from a determinate plant grow and produce?

Does it matter if the plant has already produced fruit at the time the cuttings were taken?

I haven't actually done this. But from all exerience with a lot of determinates I believe yes, take suckers and root them, they will develop into normal plants with the same growth habit as the parent, just like the indeterminates do. Determinates will grow and fruit again if you cut them back and feed them after fruiting. They will develop new shoots from the tips or the leaf axils. So there's no programmed 'death' to stop the plant (or cuttings of it) to renew and produce again. It wouldn't matter if the plant has already produced fruit when the cuttings were taken.
That being said, I'm not experienced enough with rooting cuttings to be able to say what condition the plant parts should be in for optimal success in rooting. I've had lots of indeterminate prunings that rooted like crazy in the middle of the summer, some of them were even flowering at the time, and a few also set fruit while rooting in a bucket of water. So for what I've seen, it wouldn't matter if a shoot is vegetative or if it has flowers. I'm not sure about a shoot that already bore fruit, I would probably gravitate to something more juvenile.
I had really poor results taking cuttings from plants late in the season. Those always seemed to be harboring some disease spores or they just didn't have the energy to root in late autumn with the days already too short. So from my experience, the time of season when cuttings are taken could have an effect. YMMV completely in such a different environment - you don't have the big swing in day length that we do.

Yes you can start new plants that produce from determinate tomato plants. It does not matter if it has fruited or not but I suspect that a sucker with new growth would be easier to root than one that has fruited. It would be in it's growth mode already and would not need the kick start that a fruited one might need to start rooting and fruiting again. Either way, it will work.

Thanks, I thought suckers would grow but wasn't sure since I don't grow deteminates.

Determinate are supposed to have the "self pruning" gene. That just means that growth stems will terminate and stop growing.

If you find a sucker, with a growing tip, then you should be fine. That's my understanding at least

suckers will produce along with topped plants
I did that with silvery fir tree and red robin tomato plants

I thinned out some seedlings that were growing in a clump and put the cuttings on top of a container with 1 plant but kept them wet.
Just laying down on top of the dirt some cuttings set roots and like the bee gees song stayed alive.