Sure you could. They are harder to fill at a stream than a rigid bottle, but it's doable. But having a rigid bottle along would make it easier.
Forever, I've done the following when chemically treating my water in a bottle:
Put in a tablet / drops. When dissolved, I invert the bottle, unscrew the lid a little until I get a dribble, then tighten it. I do that so everything, including the bottlecap and threads are exposed to the halogen. Okay, it's being anal-retentive, but anal-retention is better than dirrahea.
In a bladder you have much more volume of water in the drinking tube. Mostly what's there is already treated from the last filling. And maybe the water swishes around enough that there is enough mixing of dissolved chemicals. But between the bother of filling a bladder and my uncertainity about complete treatment, I use bladders only for 2-3 hour trips when I fill only at home.
I do make an exception when I'm being the sherpa for a large group and carrying a few gallons of water. Then I may use a 2.5 gallon / 10-liter bladder in a nylon bag to haul a lot and I'll toss in 10 tablets to treat it. But it doesn't have a drinking tube, just a wine-in-a-box rubber nipple as a valve.