I used to play an online global-role-play strategy game similar to Diplomacy, and when a Player pulled a move like this for the reasons you guys are describing, we called it getting a case of SuperSyphilis (in reference to cases when real-world leaders have contracted syphilis and it drives them batshit insane). Just a totally stupid, unlikely-to-work move which the GM would either force the player to change for the sake of continuity or else just facepalm and let it go through just to let the player destroy themselves.
I'm not saying that what you guys are suggesting isn't what's going to turn out to be the case. CCP's lore department has a strong and healthy reputation for coming down with the SuperSyphilis.
I am saying that "freeing up resources" for the Black Eagles by causing the most valuable military alliance that the embattled Federation has to become its enemy is a pants-on-head retarded idea. The Federation hasn't been doing superbly, you know. They only just managed to get a hostile Titan out of one of their star systems after Three Years. Their capsuleer militia may be doing well at the moment, but I remember the time when all of Gallente Warzone space was Squidspace, and anyone in power will as well. If the Black Eagles want more cash, I assure you they can squeeze it from the Senate under 'undisclosed expenses' (like every single respectable real-world intelligence agency already does).
Additionally: Silas and Vikarion: Of course the Republic has no plans to pay back the money the Gallente are paying them, nor are they exactly going to roll over whenever the Gallente tell them to just because the Gallente is the Hand That Feeds. However, the Republic's welfare does rely heavily on Gallente aid, and the Republic's politicians' careers rely on the continued good health of the Republic's Welfare. Now that is going to give the Republic's Tribal Council pause. Nobody — and I mean nobody — in the Republic wants to see the money dry up. That money allows the Republic to keep on ticking without actually having to shave wages, drop employment, lose voting bases, etc.
In RL, China made the previous Great Leader of North Korea shut his mouth (he was doing the same missile-rattling that his son is doing) by cutting off their oil pipeline. The United States has caused drastic domestic policy changes in other nations by threatening to cut off the huge amounts of money it hands out as part of its foreign policy. Europe is threatening Uganda over their Kill-The-Gays law with the same thing.
Additionally, given that Shakor, Mr Warlike, is in charge, I cannot see why the Fed would want to strain relations now, while everything is going smoothly. Midular's peace was in minority, Shakor's war stance was dominant and also he's now got more power than she ever did. Peace with Amarr is not a likely situation — the Minmatar have been doing far better in this war than the Gallente have. Sending a message to pacifist politicians is something Shakor might do, but the Fed? I strongly doubt it.