Interesting hypothetical. My research on “King Cotton” and the abolition of the slave trade indicates that England would have been very unlikely to intervene on behalf of the south. Southern media and propaganda lobbied for this, but I don’t sense the European powers were watching developments with an eye to intervene if the South did well–they had their own entanglements. They may have been rooting for the Union to lose or at least take some knocks (divide and conquer, retard a future rival), but the risks of a failed intervention were two-fold; eventual defeat of the South anyways PLUS alienating the presumptive victor.
Setting those risks aside, the South was WOEFULLY unprepared for a premodern war. That’s not just hindsight–the South was politically and economically divided, had little industry, few railroads and rolling stock, no steel, could hardly make swords much less gunpowder and firearms. It also had serious problems with a distributed leadership, no coherent financial or economic policy, rivalry and different goals between the states–it was exactly as described and advertised; a loose confederacy of interests and states that was begging for a humiliating defeat. Part of this resonates today; the South also had no coherent MORAL raison d’etre–the promotion of slavery and class inequality felt outmoded even in the 1820s and 1830s and that doesn’t win you friends and supporters. It was not a populist rebellion, like those of 1848…that was the zeitgeist of those times.
About 50,000, landed directly on Washington, preferably by UFO to avoid interdiction by the Union Navy. Any direct support of the south would have created a similar problem as the revolutionary war—the British Navy was their strength and the occupying Army was a liability, creating resentment and support for the other side, a target for harassment and interdiction by the Patriots, and easily isolated and cut off whenever it ventured away from the coasts, cities, ships and loyalists. That dynamic meant that the British had to raise the stakes over and over, committing more and more resources to defend their initial investment; in other words a hopeless boondoggle the likes of which the British (and other European powers) were not eager to take on. An unsuccessful and ongoing adventure carries great risks whereas sitting back and watching things develop carries very little.