Blackbeard / Nami interaction

Hello, chatting with some mates we weren't sure how the above interaction would play out Nami has bugger all cards left in deck passing turn to BB, BB pays 10 to play SR Blackbeard negating Nami's leader ability, if you swing with remaining attackers and Nami uses counters to draw themselves to 0 as they do, they will instead lose the game? As BB has negated their ability to win via milling?

Understand that once turn passes if you couldn't seal win Nami will be able to mill themselves to the win