Not at all! The AO+ Restorative Mist is not a replacement for soap. We just want to help society understand that there’s a difference between "clean" and "sterile." Our obsession with being as clean as possible has generally resulted in removing all bacteria from our skin, including the beneficial and necessary ecosystem that is our skin microbiome.
When it comes to soap (or your favorite make-up, moisturizer, sunblock, etc. you-name-it), while it's unlikely we've tested the specific product you have in mind, it's okay to use products that are not compatible with the Mist, so long as you remember:
The important things are the regular application of the Mist and application at night, when the Ammonia-Oxidizing Bacteria (AOB) have lots of time to operate (they like sweat, and you sweat a lot while sleeping) and when you have little else on your skin (or after anything you've applied has absorbed).