Sure. They wouldn't even necessarily have to increase their offer over what was made before free agency.
If the O's were willing to spend whatever to keep him, they would make that offer when they still have control.
And whatever offer they made, it wasn't enough... because Henderson went to FA.
So then he's in FA, and the O's are then going to make the largest offer?
Henderson doesn't know what the ultimate biggest offer is until he hits FA, because he can only talk to one team. He turns down 12/$600M before the season because he thinks he can get more or at least get that if he waits. So he waits. Free agency comes and nobody offers more so then the Os offer becomes the biggest and he accepts, if it's still on the table.
Again, wildly unlikely. But we're comparing it to a really high (or low) bar in your mega-massive shorter term deal.