Blowing up by mouth can promote mold and bacteria growth inside the pad, and put moisture inside with the air, which can reduce the insulating property of the air inside. Dry air insulates better.
All that being said, I'd bet that nearly everybody who uses a Neo-Air blows it up by mouth. So, that's how they are really being used in the field anyway.
If I worked at the store, I would forbid blowing them up by mouth in the store unless I had some suitable way to ensure sanitary safety conditions for anybody doing it. Sharing mouth nozzles wouldn't be my cup of tea.