No. Categories, tags and WooCommerce product categories are handled the way pages are. Rename Shoes to Footwear and /product-category/shoes/ redirects to /product-category/footwear/, marked from a renamed category in the list. Rename it again and the first redirect follows, so there is never a chain.
Moving a category under another parent, or renaming a parent, moves every category underneath as well, and each of them gets its own redirect. The same happens when you delete a parent and WordPress moves the categories under it up a level. Delete the ones under it at the same time and each of those goes onto Broken links at its old address instead.
Swap two categories' names, or give a new category an address an old one gave up, and the redirect the old rename made for that address is deleted, so the category living there now answers. A redirect you wrote by hand for that address still wins, and so does one a rename made that you have pointed somewhere else: delete it under Redirects if the category should answer there. If a redirect of yours sends the new address back to the old one, no redirect is made the other way, so the two never send visitors round in circles.
It is the same switch as for pages, Keep the old address working when a page is renamed under Settings → Renamed pages. On a site with plain permalinks, a category's address (?cat=12) does not change with a rename, but a tag's (?tag=winter) and a product category's (?product_cat=shoes) do, and those are not kept: choose any other setting under Settings → Permalinks to have them kept.
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Redirects
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