No on several accounts:
A possessing fire spirit has his Energy Aura active, but that doesn't actually do anything except if the spirit attacks in melee or is hit by a melee attack. That is all it does. Gear is not affected as far as the rules are concerned.
But be aware that elemental spirits aren't actually immune against their own element. Manifesting spirits do have their hardened armor against mundane damage sources, but nothing more. A possessing spirit doesn't even get that protection. So it is entirely possible to douse a fire spirit in gasoline and watch it burn to disruption by RAW.