Unfortunately it is not an option. My scientific wild a** guess (SWAG) is that at one time we used to require passengers to take a sip from their drinks whenever they carried one into the checkpoint that could not be sealed and sent through the x-ray. If you recall, TSA got a lot of heat from the urban myths regarding a little girl who drank from a cup that had a frog inside of it and the woman who allegedly was forced to sip her own breast milk. At any rate, I think this is probably the reason why TSA won't allow the option of drinking the liquid at the checkpoint.

And she was, in fact, given the standard option of leaving the checkpoint to empty the cup and then return (after re-screening). Just to give you a little insight, 99% of the time, passengers opt to abandon their cups, drinks, containers, etc. at the checkpoint rather than go through re-screening. A fair number of those people later complain that they were forced to give up their cup, drink, container, etc.