I think it reasonably likely, and I think the most immediate fallout is likely to be a resounding "sproing" as the golden Amarr fleet meets the hardened defensive structure that is The Citadel and is predictably repelled. Invading the civilization-level equivalent of a reclusive survivalist compound is not likely to go well absent overwhelming force-- you can depend on the residents to abruptly forget their differences and pick up guns.
The really interesting question is why the Amarr would have some semi-reasonable cause to think that it would work and be worth it. I've already held forth on that topic a good bit today; my brain's getting tired.
Edit:
Reposting. In addtion to CCP's need to maintain the storyline balance of power so that it doesn't have to rewrite everybody as conquered puppet-states of the Amarr (or anybody else):
* There's currently no other trouble between the Amarr and the Caldari, though something could come up in the course of winding up (please God) Heth's storyline, so these rumblings in the Empire seem like dark omens. Alternatively, the "Reclaiming" saber-rattling could be the equivalent of a static charge waiting for something to ground it-- like a Heth-related lightning rod.
* The Caldari are not Amarrian believers. They are heathens, and must, according to the more conservative Amarr (as well as others if pressed), eventually be Reclaimed for God one way or another.
* The State is currently in a state of disarray verging on civil war.
* The border the State is watching is not the Amarrian border. Warnings about the Amarr from various State loyalists have gone largely unheeded-- and even such loyalists normally assume that the Amarr would not attempt to Reclaim the Caldari unless the Federation and Republic were no longer threats.
* Really conservative Amarr have a bad tendency not to fairly weigh the strengths of other cultures or their militaries. "Have faith. God will grant victory to our righteous cause!" is an excellent stand-in for careful strategy where morale is concerned, though not so much in terms of practical consequences. IC reactions to Vak'Atioth suggest that the Amarr still have not fully adjusted to living in a world where they cannot steamroll everybody in sight, and CCP has a demonstrated tendency to pick up IC tropes it likes and run with them.
* The Federation and the Republic are now on the outs; the Amarr may very well sense an opportunity to roll up all three of their competitors, one by one-- but the Federation and Republic are on guard against Amarrian incursion, and the Amarr will need a lot of additional forces to guarantee victory against either one singly. Pity the Caldari war effort has stalled and they're wrapped up in their own internal power struggles. "Oh, wait. We can do something about that."
* There may be certain plans within the Empire that the Amarr believe could place the Caldari State into their hands with minimal loss of power or war material-- especially if they can seize the center of power and ensure that the CEP (or Heth, or both) are dancing to their tune. They demonstrated in their handling of the Minmatar that they have no qualms about turning existing power structures to their advantage.
* Net result: massive but arguably understandable miscalculation with terrible consequences for Caldari/Amarr relations: even if the Amarr seize the whole CEP, the Caldari people aren't going to recognize any leadership under the control of a foreign power. The Caldari pull together as they tend to in times of crisis, and the Amarr incursion finds itself facing the full military might of The Citadel. House Sarum withdraws with heavy losses. The Caldari State formally withdraws from its alliance with the Amarr and fortifies that border, as well.