Here’s a quick graphic to visually answer the question: does the putt count as “in,” or not? Unfortunately, holing-out has more specific requirements than one might think.

The official rules from the PDGA read as follows:

802.05 Holing Out

A. Basket Targets: In order to hole out, the thrower must release the disc and it must come to rest supported by the chains and/or the inner cylinder (bottom and inside wall) of the tray. It may be
additionally supported by the pole. A disc that enters the target below the top of the tray or above the bottom of the chain support is not holed out.

Hope this helps!