Don't bet on it. My experience during the first Gulf war...based on direct contact within arab Christian parishes...indicated that a significant percentage of arab Christians in this country opposed our intervention against the "ghoulish" Saddam to save Kuwait and Saudi Arabia. Their ethnicity seemed to trump their Christianity.
Shared ethnicity probably had very little to do with it, as most Iraqi Christians are a linguistic as well as religious minority (Most of them speak Aramic as a first language), and many of the Christians are regarded as "foreigners" whose ancestors came into Iraq from elsewhere (which is true for the Coptic and Orthodox Christians, but not generally true of the Nestorians and Chaldeans). More likely, it's because they regarded Saddam's Baathist regime as a bulwark against Sunni and Shiite factions in Iraq, both of which they perceived as being more hostile towards Christianity.
The biggest downside to the American liberation of Iraq is that the Christian populace will probably all have to choose between martyrdom and relocation to Chicago. (I pick Chicago because the Nestorian patriarch has had his seat there for years.) It's looking out for the interests of their coreligionists back in the Old Country that make Arab Christians wary of American intervention, not siding with their persecutors, nor disloyalty to the U.S.