No problem
When in coach, I always bring my own mini bottles thru security. Never any problem at security or with discrete consumption in coach on board.
I was aware that FAA regulations provide that the cabin attendants have to pour for you (supposedly so that they can monitor for possible overconsumption, a possible "safety" concern).
The more interesting issue is consumption of duty free liquor on board. On a recent trip back stateside from Cancun, I consumed half of one of my bottles of tequila by simply sticking the neck thru the "bonded" bag that you are given when boarding. Is this a customs violation?