What you're talking about is, of course, beyond the science of today. But if, in your story, the science of gravity is far beyond ours, then, why not?
I am going to come at this from a safety and logistical standpoint rather than a science standpoint, because really, you can do anything given the right tech in a fictional universe. I know, I know, this has a physics tag, but there are more barriers to this than just physics. You asked if it was possible, and I am going to come at it from a slightly different angle.
The outer edge of the ball would have to have considerable tension--enough that there shouldn't be dispersal from the swimmers if it's going to work at all. EDIT: Thinking about this, it should be multi-layered, in order for people to be able to swim: layer one is the outer "harder" layer from which nothing escapes, except for release points, maybe on the top and perhaps the bottom. Layer 2, the inner layer, takes care of the splash and release of bubbles and physics of swimming action, most of which bounces back off layer 1, if it's water.
I would recommend that swimmers have breathing apparatus, because once they are in the ball, they would be under water. It sounds as though you are wanting surface swimming to happen, which should not be possible in this model, unless you are willing to have the top part be flat, like regular water. Otherwise, you risk drowning people, because if it's held together in this way, pushing through the surface tension should be very difficult for swimmers. Even if it isn't, most people would have a very difficult time orienting themselves in the ball. I can see people drowning just because they "got lost" and were disoriented. There's also nothing to push off of, no bottom...If there's a way to die, people will find it...
There are some logistical problems with no structure touching it. How would the people actually get into the water? The surface of the the water would have to managed minutely, so if you are also planning for people to "float" through the air to get in, that might be a problem. There could be a diving board above, but once they are in, how do the poor sots get out?
Here's how I would have it set up: ball 'o water about 5-9 feet above a regular pool. So maybe they dive in above, and then push out, landing in the ordinary water below. The pool beneath would have to mostly be for exiting the ball and not for any other purpose--OR you could have an enormous regular pool where people can swim in the ordinary way, with a part sectioned off, used just for exiting the ball 'o water. EDIT: So there should be exit/entrance points on the top and the bottom of the ball in case of emergency. This definitely would be controlled, like any slightly dangerous activity such as rock climbing, caving--that sort of thing. I don't see it as something that everyone will want to do or be capable of doing. Time in the ball would be regulated and supervised necessarily.
For safety purposes I would
- Have several life guards inside the ball (They would also tell swimmers when to get out, before the breathers run out)
- Have each swimmer inside the ball be issued a re-breather of some
kind that is difficult to lose, as well as goggles.
The people swimming in the ball would be of the adventurous sort--like the sort of people who do zip lining. It would be kids above a certain age, they would sign waivers. I see this as a sort of luxury resort "experience" like those rock climbing walls you find on cruise ships, except more unique. It also adds to the experience of the swimmers in the ordinary side of the pool, because they can look up and see this marvel.