The way I see it Ravs is that both the UK and Australian forces are in Iraq for the exact reason you are 'concerned' about.
IE to strengthen military ties with the US, and ensure that when we need their help, and we will need it sooner or later, that the US has no qualms coming to our aid.
Maybe not so much with the Brit forces, but thats pretty much why there are Diggers in Iraq right now IMO(also why there were Aussies in Vietnam, Somalia,Rwanda, Afghanistan etc.), Australia as a nation simply could not afford to do anything but fight alongside the Yanks, having a relatively small population/defence force, and living just south of the world's largest Muslim population, a great deal of our national security in current times lies in the fact that you mess with us, you have to deal with the US military machine to, not just ours.
I think that relatively recent events down here have more than proved that America is indeed capable and willing to offer military assistance to her allies should the need arise.
Every time our neighbours get a bit noisey, a US carrier battle group shows up for exercises with the Aussie Navy in our northern waters.
Nothing like a water borne Death Star and a few thousand Marines to even the odds a little.
Anyway, if the Black Watch are moving north, and that bunch of well 'ard lads are 'up for it', life as an insurgent in their AO certainly isnt going to get any easier.
Brits