The Sabres draft list was already built.
No North American league has played since mid March. The scouting staff had nothing to do but work on draft prep since then until they were fired (about 3 months). Add in the NHL toying with the idea of having an early June draft (that idea was still alive as late as mid/late May before getting scrapped) and there is very little chance the Sabres draft board wasn't already put together. They needed to be ready in case the NHL decided to go ahead with that early June draft.
That completed work would be Sabres property and available to Adams if he wishes to use it.
If I got a job as a GM with months to the draft, I sure wouldn't want the draft list of the guy who just got fired.
So while there may be a fully fleshed out draft list, which I really doubt as Botterill never talked about having those meetings with his scouting staff, none of those conversations involved the guy that is building the roster and the prospect pipeline moving forward.
If Adams values very different players than Botterill did, that draft list isn't of a whole lot of use.