Yes you can. You have to use a very dry mix to cut down on the slumping. Too wet a mix and the bottom edge could be quite thick. Rough up the sides of the plastic bucket before you start to give the hypertufa or concrete something to grab on to. Depending on the temperatures there (or kids that like to climb), you may want to give extra adhesion by cutting slots in the bucket and making wire screen "T" shapes. The top of the "T" would anchor to the concrete that you pour inside the bucket and the leg of the "T" would act as a "tie" or anchor for the covering on the outside of the bucket.
You may want to work on this in the place where the feeder is going to be permanently, due to the weight. Work in the shade if you can, use a spray bottle to help keep it moist and cover with plastic for a few days to help slow the cure. Good luck. Billie

Great info. Thanks. This will be my first tufa project, but what the heck!
I'm hoping to have it done by next weekend.

One more suggestion would be to pour and let set the concrete inside before you do the tufa outside. This way tufa can be joined and sort of hung from the concrete to help support it. I would advise working from the bottom up and if you have problems with slumping stop and let it set up for a bit before continuing up the sides. If you ad bonding agent to the mix the new will adhere to the old, as well as to the concrete on the top. You could also use chicken wire around the outside of the bucket to help support it, especially if you want to finish it in one day. Hope this helps and good luck with your project!