No, he drained it empty, then handed it back to Cocoa. The heat must have made him real thirsty. Well, he'd been out in it presumably more than Lacuna had been.
"H-Here... I'll go get you a refill," said Cocoa. He rushed off to do just that. If Lacuna wasn't mistaken, he actually seemed a bit relieved. He wasn't sure what else he could do to help, but at least getting Fluffmutter another drink was something he could definitely do.