No it wont.
Destiny Bond's effect only works if the move is used immediately prior to fainting. Thus, if the user takes another turn, the effect disappears.
Using Explosion will count as 'taking another turn,' so Destiny Bond will wear off before Explosion knocks your Pokemon out.
Also, just another flaw in this theory, but Destiny Bond will cause the Pokemon that knocks yours out to faint. However, using Explosion means your Pokemon makes itself faint, so it wouldn't affect them anyway, as they did not land the finishing blow.
So a nice idea, but it doesn't work in practice.