The Icanus is simply a demonstration of the Tarkin Doctrine: rather than expend massive amounts of resources enforcing the peace person to person, simply construct massive displays of force that can be used to discourage and thereby prevent any opposition. The Icanus was designed not as a viable tactical unit, but as a political weapon to discourage enemies of the EA while at the same time instilling patriotism within the hearts and minds of all members of the Alliance. Not unlike the Death Star, the Icanus is "cold, efficient, and promotes an understanding of fear, proving to be more powerful than military power alone".
The Nemesis was an extension of this, but more geared towards creating a vessel that serves both masters; political suppression/propaganda and an effective tactical unit. In constructing the Icanus, the EA simply moved the counter further towards the political side of the spectrum.
Now, we don't know how dedicated construction was for the Icanus, but it's not inconvievable that an apparently rich, prosperous system with a well-established industrial base could build such a vessel in the alloted time period. Granted, the civil war could effect that, but the repressive and Soviet-esque style of the EA means they would have no qualms about diverting resources from civil projects and the like to help in constructing the behemoth. Obviously there can be no comparison to the GTVA here. The vast differences in government, population and ethos alone render any direct comparisons moot, and given the vague nature of the general storyline, one can't make snap decisions 'just because'.
Indeed, not only is it possible that the Icanus could be build by the EA in the time specified, but I would even go so far as to expect the Alliance to attempt such an undertaking.