Q.Honeysuckle vine
I have a honeysuckle vine that has grown into a bush and the vines cascade across a wood fence. There are some sprouts that have come up on their own around the base and I’m wondering if those sprouts can be transplanted and, if so, will they grow into a bush?

Here are some articles that will help you.
https://www.gardeningknowhow.com/ornamental/vines/honeysuckle/prune-honeysuckle-plants.htm
https://www.gardeningknowhow.com/ornamental/vines/honeysuckle/japanese-honeysuckle-weed.htm