They wouldn't have to intervene in any major way. Simple recognition coupled with the smashing of the Union blockade is going to implode the Union economy.
Yes, they would have to intervene in a serious way. As the deployment of (presumably?) a not insubstantial portion of the Royal Navy to break the Union blockade and a resultant quasi-war at sea with the U.S. (at the very least, if not outright war as the Union threatened) seems to be intervening in "a serious way". But to tackle a more fundamental assumption, does recognition necessarily beget a breaking of the blockade? Britain, throughout the Nineteenth Century, maintained a consistent position with regard to belligerents' rights at war. And blockades were very much a legitimate part of a belligerent's policy toolbox, a position which Britain had been aggressively defended since the Napoleonic Wars. Recognition would not,
ipso facto, require Britain to smash the blockad
e and to do so sans an alliance with the Confederacy would constitute abandoning a long-held hostility to neutrals' rights. (...though that honesty would be an interesting timeline, in which the South is saved by Britain's adoption of the American position on the issue which sparked the War of 1812.) And it's by no means impossible Britain would choose to ally with the Confederacy, though I think all recognition would yield is studious neutrality and an offer to mediate an end of the conflict. The point is that there're a half-dozen steps between "simple recognition" and "smashing the blockade" that need framed out and contextualized, which the reader should be shown but usually isn't.
There's going to be a run on the banks, British firms will quit loaning American banks credit and the Union banks will have to call in their loans which will be disastrous, inflation is going to skyrocket, massive desertions will hamper the war effort, there won't be any Union imports of powder or guns, specie will quickly be the main currency accepted.
This is a perfect illustration of "
something something foreign recognition
something something profit". Why are British banks, for instance, going to stop lending to (Yankee-)American firms? There's certainly no reason to stop cold turkey unless Britain's gotten itself into a shooting war with the United States. Which is by no means impossible in the event of recognizing the Confederacy. But it requires the U.S. to affirmatively initiate hostilities -- as Union diplomacy threatened to do in the event of foreign recognition -- or it requires Britain to purposefully ally with the Confederacy. If it's the former, there's going to be a ferocious and acrimonious debate as to whether to make good on the Union's threats or to "accede" to the foreign recognition and find some other way to make the recognizer pay or otherwise extract revenge. A debate that should be front-and-center, to show the reader how this major divergence from OTL came about. And if it's the latter, the same need to show the course of events that led to it needs to be front-and-center, as Palmerston was a vociferous advocate of British neutrality.
All the while the CSA gets massive access to foreign credit, imports of arms, access to New Orleans, a big morale boost. The list goes on and on, but it would be a legitimate disaster before the first soldier was even killed. I think people severely underestimate how badly the Union economy needs a friendly Britain to prosecute a war.
You are absolutely right re: foreign recognition being a blow to the Union cause and it usually being underestimated how important a non-antagonistic Britain is. You're also right about recognition being a shot in the arm for Confederate morale and that, in theory, it'd open up access to more foreign credit and arms imports. (I am unsure how much that would actually come to pass in fact, as the facts on the ground will dictate the willingness to lend to the Confederacy. And, as said above, foreign recognition does not
ipso facto mean the destruction of the blockade.)
But I am going to focus on the bolded part of that statement. And ask a simple question: If recognition happens after April 1862 -- as it does in most timelines --
how does it yield access to New Orleans? As by then it's been occupied by Farragut. Even stipulating that Britain breaks the blockade, that doesn't restore New Orleans to the Confederacy. Does breaking the blockade somehow allow the Confederacy to raise an entirely new army for the purpose of retaking the city? Does the Union abandon it or seek a negotiated evacuation? Or does Britain eject the damn yankees by force? I feel a bit like a math teacher insisting that you show your work, but New Orleans logically returning the Confederacy as a result of foreign recognition reeks of being ASB without some bridging context.
Getting intervention is tricky, but if it happens the war is over full stop. How the borders shake out is anyone's guess though. I'm tempted to say that there's a great many plebiscites in the border states and the Canadian border probably moves very little if at all though.
I would say that depends upon how one defines "intervention" -- as I'd argue foreign recognition would constitute "intervention" -- but if the "intervention" is one or more European powers declaring war on the U.S., you're probably right. With regard to plebiscites, given what happened in Kansas, the Union is going to be emphatically against a plebiscite in any state that has a significant slave-holding population. And would probably insist that all individuals -- including slaves -- be allowed to vote, which would be a non-starter for the Confederacy when determining the fate of Tennessee or the Virginian Tidewater. ...and why would the Canadian border move at all, unless you were expecting things to go full Trent War with the inevitable invasion of Canada?