I'm not sure. Submarines are the kind of weapon the Royal Navy wants to keep underdeveloped, judging by its OTL response to when they were actually becoming useful.
Not to mention that that the submarine had a terrible record even before its final mission in terms of killing crew but not enemies:
http://www.charlestonillustrated.com/hunley/#
It's intriguing, but the idea of causing anything to be sped up by 50 years is far fetched.
RN was fine as long as submarines were "Day Time Torpedo Boats", seen as only useful in harbor, coast defense. The RN had a bit of blue water snobbery, they accepted some brown waters being hard to attack, as long as the deep blue was British. Bit of over simplification, but largely reflects the attitude of many. It is hard for people to get their mind around, but building more torpedo boats and U-boats would have made the British more comfortable with the High Seas fleet, even if the capital budget was unchanged. Trade a couple of battleship for 100 more U-boats, destroyers, or Torpedo boats, and a lot of the tension goes away.
It's an intriguing idea, but i suspect it will run into a couple of problems. First and foremost, how good was this vessel reallky? It could dive, all right, but what about its performance? how many miles out to sea could it operate? Could it catch up with a target under sail or steam? How sure would a successful attack be to actually sink the target if it was, say, a full-sized frigate or iron-hulled steamer rather than Housatonic?
Submarines will not stay invulnerable for long. The nineteenth-century mind was quite prolific when it came to gadgets. I don't think either side in the ACW could deploy anything like Whitehead torpedoes, but mines, primitive depth charges, booby traps or even heavy objects dropped from yardarams could do damage to a vehicle that had to come so close to attack. Not to mention the damage a single shell would do if it could be made to burst on the surface of the water over it. If I was a union admiral, I'd start patrols on steam launches armed with hand grenades and harpoon guns. Unless Hunley's next boats are a lot faster and can dive a lot deeper, that would take care of that problem.
Reliable - had huge issues. In software terms, it would not even be a beta version, think Alpha version of totally new category of program. It was hand cranked, suffocation was an issue, visibility is horrible, etc.
It performance was a few knots, it range was maybe 5-10 knots. The attack it did took all night. It successfully attack, and made it most of the way back to port, then sank, probably do to battle damage or flaws in the design. Seems like it also sank on a previous trial, and took all lives aboard.
It could not catch a row boat, much less a moving ship. Useful to keep ships from anchoring too near a defended port.
All a union admiral would have to do not anchor his ship right next to a know harbor with a submarine. It is a little more work to keep the ships moving as opposed just to anchor outside of cannon range, but the counter measure is easy to implement. Now give a few years of peace time development and a good budget, it might have become a better weapon, of very limited usefulness. That is, it could keep enemy warships 10 miles from a port. But without also inventing a torpedo, and finding a non-human power plant, it was just not that useful. Trained swimmers with a neutral bouancy mine would have been as effective.