Does the air have an aura?

It pretty much depends.

Not in the traditional sence, no. The air contains elemental energy that can be felt during meditation excercizes and the feel of the energy will change with wind speed and particulate matter but any creature or item with an aura will commonly overshadow it unless you're specifically trying to channel the element.

Unless you're specifically going to to somthing that requires you to use eather energy you're better off just going outside and feeling the air on your skin or other physical sences.