Official Ruling
No, you can't. If the same reference to a "played" trigger condition being performed isn't being made for an effect when it has a "when X is played" trigger condition, the state when the effect is processed will be referenced. In this case, because the Digimon that could be referenced by this card's [All Turns] effect was removed, you can't delete a Digimon.
Source: BT17-076 Eosmon