I suggest that, for most questions, the answer "it depends on your world" is banned, as it doesn't answer anything since it applies to everything. Instead, people could tell how it works in their world/game and explain the logic behind it? >_<
As far as I understand it, in LoTR, Fair Elves are godlings or at least beings similar to angels in Christian mythos. As such, their aura is an aura of power, a manifestation of their "angelic" state (the way angels are usually described as surrounded with an aura of divine light). The first answer to the question at hand IMO is: why would a Fair Elf even try to hide his aura anyway? Do you think that angels would hide their angelic nature to human beings? The same way, the Lordly Elves would probably not.
As for how much of a bonus that gives to fire at them, well... if you were able to resist the awe they inspire, you probably don't need any bonus anyway.
At last, in worlds where Fair Elves aren't the majestic, god-like beings they're in LoTR, they should not have such an aura so there's no problem with it.