AFAIK, no code holds that a ball OVER DBT is dead: it is dead only after touching DBT. So a fielder may legally catch a fly ball provided that neither he nor the ball has contacted DBT when the ball is caught.
If the fielder subsequently enters DBT, it's "catch and carry" -- the BR is out, the ball is dead, and other runners are awarded 1 base.
The issue of whether a fielder may throw the ball from DBT is moot, since the ball will be dead.