It's not implausible. If the CSA industrialized, conquered parts of the Caribbean and Mexico, and then maybe won a few more wars with USA while Union was in troubled times then maybe, just maybe. Alternatively you could have the USA fracture and split allowing the CSA to become dominant in North America.
While the CSA was industrializing, it was doing so at a significantly slower rate than the Union. The massive debt they used to fund the ACW left them in worse financial shape than the modern Greek debt crisis. They were also very immigrant-unfriendly, and so lacked the population for heavy industrialization.
Much of the CSA was expansionistic, but every attempt whether by force or diplomacy, to obtain territory from the US or Mexico, failed. The CSA lacked the force projection abilities to take and hold New Mexico Territory, let alone parts of Latin America. Invading Mexico risks war with France in the short term, as well as the Union.
There's also the problem that the Confederacy was founded on the idea that any state can leave at any time for any reason. Every issue, every election, risks the CSA losing states or even fragmenting.
The Confederacy has no chance of becoming a superpower and is extremely unlikely to become a great power. If they do very well, they might become an important regional power, but even that's optimistic.