This only works so long as the atmosphere being displaced weighs more than the balloon plus the payload. As soon as the air gets thin enough that the weight of the balloon+payload is equal to the weight of the air that would fill the volume of the balloon, then it stops rising. (Or, more likely the balloon rips open because it expanded farther than it could stretch).
Usually, this is really high in the atmosphere, but it's definitely not space.
This is all ignoring that orbit requires going sideways really, really fast (so fast, actually, that it requires falling, but going sideways so fast that the earth curves away and you miss).