Actually, ZV, that "in process" icon at the top left only applies when you are sitting in a chair, not when sitting on the ground.
There is a "sit and drink" animation, so that one might be possible. As for eating...well, there's really no animation at all except for the "use unique power" animation.
Of course, this may be one of those deals where the Bioware engine has that thrusting hand motion hard-coded, which effectively breaks the animation you're currently on (i.e. sitting). *shrugs*