here is a DH2 Bomber
http://www.fiddlersgreen.net/aircraft/Airco-DH4/IMAGES/DH-2-Bomber-British.jpg
A symbol I can understand, its needed to identify friend from foe. But why such a gaudy one, its so visible that I hypothesized that it was a taunt to enemy airmen.
It isn't a target, it's a roundel. They're national symbols often found on military aircraft, and some flags.
As yyc_guy says, it's a roundel and not a target, and they were used for identification.
The fact that it's so visible is part of the idea. You can liken it to earlier military uniforms; British wore red, Austrians wore white and Russians wore green. This was all to make sure that you were shooting at the right people.
Back to aircraft, remember that they were flying at a decent altitude above the battlefield. Both the roundels and bright uniforms of the black powder era had a visibility problem to overcome. For musketmen it was smoky battlefields, for planes it was the fact that you were moving at a high altitude. This meant that they needed a large, easily visible way to show whose side they were on. With the red-white-blue colour scheme that didn't necessarily imply that the plane was British but that it was on the Entente's side. Same goes for the iron cross used on German and Austro-Hungarian aircraft.
Also bear in mind that not only the British used this. The French used the same colours but inverted (so blue centre and red outer), the Italians used red-white-green and the Central Powers, as said before, used the iron cross.
Regarding your hypothesis, I think it's highly unlikely as they were in use by the start of the war, where planes were initially used for just reconnaissance; air-to-air combat didn't really become prevalent until later on.
It's not like you're working to conceal your planes, and anti-aircraft fire is hardly accurate. There's no real reason to try and disguise your aircraft, better to easily distinguish friend from foe than just have a mess of planes shooting it out blindly.
