Official Ruling
Yes, you can. When the opponent's Digimon is played by an effect, this card's <Delay> effect and BT15-081 [Leviamon (X Antibody)]'s {Trash} [All Turns] effect will trigger simultaneously. You activate this card's <Delay> effect first and play EX5-063 [Leviamon] from the trash. EX5-063 [Leviamon]'s effect derived triggers, then BT15-081 [Leviamon (X Antibody)]'s triggered {Trash} [All Turns] effect can digivolve EX5-063 [Leviamon] into BT15-081 [Leviamon (X Antibody)].
Source: EX5-069 Biting Crush