I do hope for Drake’s sake that he is able to get involved in Koby’s rescue simply due to being his fellow SWORD member and perhaps other SWORD members as well as one can only wonder when all of SWORD info will be known to us. Of course to also give him more spotlight after his disappointing showing in Wano
It’s very likely Drake is alive and so, he could potentially see the newspaper. I’m not certain the Marines would send people after Koby to rescue with Akainu heading it but SWORD could on that note. It’s an opportunity, but you never know with Oda.
Otherwise, interesting spoilers.
1. I don't think coby is going to get rescued for a few reasons: a). The marines don't even know if coby was kidnapped in the first place since they were all turned to stone. So they had to rely on second hand info. B). I think coby is actually with Hancock and Raleigh but it was stated by boa sisters to the marines when they became unstoned that bb captured him. This was done since raykeigh was intrigued with coby and is planning on having him and boa train together. And more than likely coby probably contacted garp before hand letting him know what was what.
Or here is another take just incase he is actually on bbs ship
2. He is on bbs ship but wasn't captured but instead willingly joined since he wants to get Intel on what apikiji is doing. This made it easier for coby to do since based on his potential that bb would have seen in the rocky port incident he is genuinely interested in coby potentially joining his crew. So coby just using this to infiltrate.
Ultimately the marines won't get involved since they have to worry about other things however akainu regardless would be worried about perception so he uses this to forcibly motivate the other younger marines calling them weak since they weren't able to 1. Bring in a warlord and 2. We're sitting ducks having coby and the mew pacifistas do all the heavy lifting during the Amazon lily incident.
Amd sword won't assist since coby would have already contacted swords leader (garp/sen goku)/telling him that he is fine.
The only one in both scenarios that is more than likely gonna help koby is luffy since he would obvious not know what's going on. It's the set up for bb vs coby and luffy in any of the scenarios presented