The answer is yes. The details are a bit different, though.
The deal would be:
1) all the draft picks, crowder + bradley + zeller for Davis
2 ) sign hayward for $30,300,000
3) release all expiring contracts.
That gives you the following lineup, with a total salary of $102,410,456, which is under the cap.
Guards: IT, Smart, Rozier, D. Jackson
Forwards: Hayward, Horford, Brown
Bigs: Davis, Mickey
All under contract this year and next year, and next year we can max out IT using bird rights.
This team should beat Cleveland (3 allstars, 1 almost all star) and will have a long future, and will create playing time for our young players.
If I'm the NO GM, I would pull the trigger. That's a lot of picks, including your own picks that will be high lottery picks for years.
Great for both teams.