I wanted to harvest the tubers, and transplant some of them, but then I saw that they already started growing due to warmer weather than usual. I still transplanted them but many are broken or damaged where the "new growth tip" came out. Will they still grow?
It appears from an illustrations in this article that there are in fact two growth tips to each tuber, one at either end. One tip connects to the root that formed it, and from which other roots may grow (similar to a Lily of the Valley plant) and the other tip forms new roots and plants. I assume you mean that your plants are damaged at this end. If they were not damaged at the other end (especially if some of the root were still attached there), then it's possible your artichoke will sprout from that spot, as is seen in many other rhizomatous perennials. I suspect that any tubers planted with both growing points missing will not sprout, however.
Although called tubers, they are not like potato tubers that have many eyes. From the photos on the internet, it would appear that they grow from one spot only. I have not found any article that suggests that you can chop them up to make many plants.
So, I think they will not sprout again.
I can only find statements such as this
Growing Chinese Artichokes
These vegetables may only be propagated from tubers which are planted to a depth of about 75-100 mm (3-4 inches) and 225-300 mm (9-12 inches) apart. Rows should be well spaced - 450 mm (6 inches) - which means they do take up quite a lot of room.
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