Under the terms of the alliance, yeah. But NATO was specifically a defensive alliance with a somewhat narrowly defined casus foederis to which the Iraq war didn't apply, as was the Triple Alliance; there is no such beast as a casus foederis in any EU3 alliance, much less the extremely complex ones that obtained in typical eighteenth- and nineteenth-century agreements. If the alliance system is going to be reworked like that, I think that different varieties of alliance ought to be permissible, like the classic Franco-Swedish "join this war and I will give you cash monies" or specifically offensive alliances geared against a specific country with a time limit on the casus foederis (e.g. the Italo-Prussian alliance of early 1866).
Or we could have just three different kinds of Alliances:
Defensive Alliance: Only obligated to defend eachother if called upon
Alliance: Obligated to defend eachother, optional to help eachother in aggressive wars if called upon
War Alliance: Obligated to defend and to help eachother in aggressive wars if called upon