Aid spell affecting non-combatants only?

The Bless spell has this restriction:

A blessing, however, affects only those not already engaged in melee combat.

While the Aid spell doesn’t directly say anything similar. It does however say this:

The recipient of this spell gains the benefit of a bless spell and a special bonus of 1d8 additional hit points for the duration of the spell.

So, a Bless spell cast onto allies already in combat has no effect .. but would the Aid spell ignore that limitation?