Official Ruling
No, you can't. The effect will trigger on both copies, but after the attack declaration is made for the 1st [Omnimon] and effects such as [When Attacking] effects have finished activating, the effect on the 2nd copy of this card that was pending activation will activate before the counter timing. However, a new attack declaration can't be made during an attack, and only the 1st [Omnimon]'s attack can be performed as a result.
Source: BT17-081 Tai Kamiya & Matt Ishida