Aardwolfe,
The Emergency Preparedness merit badge (hereinafter EPMB) entails nine categories of requirements, of which the first listed happens to be earning the First Aid merit badge (hereinafter FAMB). A scout has one year in which to complete all the requirements of a merit badge. The FAMB can be earned at any time before the EPMB; or alternatively, earning the FAMB within one year of starting the EPMB should also satisfy that requirement of the EPMB (that assumes the consent of the merit badge counselor for EPMB).
The most common approach is to earn the FAMB before starting the EPMB, however many scouts also take both merit badges concurrently. In the latter case, the counsellor for EPMB will not sign the "Application For Merit Badge" (blue card) as completed until the scout evidences completion of the FAMB. Taking the merit badge classes in reverse order would not seem common. However, I see no reason why it could not be done that way and still meet all the requirements.
John