I am trying to think of what you mean... but having little problems. Do you mean as boyancy or as ballast? (I will assume ballast, because as boyancy you would have a one way trip...)

In water, the pump would pump water into the bag, since it can't draw air while under water...

It will fill the bag until it runs out of room, then either the bag gives (stretches) or the water stops going in. If the bag stretches then it might work, if not, it probably won't.

Assuming it doesn't stretch: Once you go to deflate it, under water, the bag won't empty; inside and outside are water at the same pressure (since you can't compress water). With this system it would only let you go deeper, but not surface.

Assuming it does stretch: If the bag itself stretched, it would force that extra water out until it is no longer stretched. To make it work with this system you would need to make the boat boyant with the bag filled to the point before it stretches, then to submerge you add extra water, to surface you let that extra go.