It's not going to speed up and promote growth as such. However as ChingazMB said, it does prevent breakage and so on. My horses live in tal bags just about 24/7 now, though you do need to be careful with your choice of bags, some will rub hair out or break it if it gets snagged. I only use Swish full length tail bags now, but I'm not sure if they ship outside Australia.
You have to be careful about using them. If they snag on something they can rip the tail right out. I had a gelding with a gorgeous tail and one of his pasture mates decided he really liked the look of that tailbag one day. Ripped it right out- along with half of the tail I worked my a off for. Couldn't have felt very good, either, poor little guy.
With that said, I still use them cautiously. My TB came with a terrible wispy tail and it filled out beautifully, nice and full, in about a year with my careful care of it. Through the sunny months I kept him in a flysheet and braided his tail about 90% of the time, taking it out very often to brush it out and apply conditioners and MTG. Beyond the horse's comfort and well-being, staying on top of flies also plays a big part in tail health. Swishing it around all the time, arguably even more so if it's braided or bagged, only breaks more hairs.
Now I mostly bag through the rainy season- all of the wetness and the dirt and mud is just no good for the tail and for my keeping up with the care of it.
I only use the tailbags that just have a single tube with 2-4 ties on the top that you thread through the braid. I've tried a lot of styles haven't personally had luck with other styles, I find these to be the simplest. You just braid the tail all the way down, fold it in half, then toss it into the tube and tie it up- below the dock, of course.
Here are some tails I've slaved over (following the method I described):
This is the pony who later lost his tail
And here's my TB. Did I mention after I sold him his new owner stopped braiding and bagging his tail and now it's about 20 hairs at his hocks again, what a shame, lol
I bought my warmblood 4 years ago and for the first year I did not bag my horses tail but after it started getting really thin I decided to try it. Now my horses tail is dragging on the ground about a foot and it is very thick. They also help to keep the tail clean. The tail needs to be taken out of the bag though every 3-4 weeks though or the tail will dry out and that can cause breakage. Also, it is best if when you rinse your horse of if you can try to avoid getting them the bag wet because the tail can mildew while in the bag. They have their pros and cons but for me the pros outweigh the cons.
Whichever you choose make sure you remember to leave something to swat at flies with.
If you use a tube sock (easy and cheap) sew some yarn strands on the end. If you knot it up with vet wrap be sure to wrap some bailing twine or yarn in there, etc.