Not gonna lie that part just seems fucking stupid to me. His other plans through the story more or less made sense, but this? Him actually thinking that he can extort the World Government into making him a King and recognizing his Yonko crew because of KOBY? And not to mention thinking this will work RIGHT after the World Government disbanded the Warlords?
The fuck is he thinking? i question them doing this if he captured an Admiral or Garp himself, much less Koby. It would be the ultimate bitch move on their part too since it basically announces to all the pirates in the world "hey, if you want to go legit and become a King/Queen? Just kidnap a semi-important member of the Marines and use them as leverage!"
Honestly Teach, the fuck are you thinking?