It would likely have a larger impact on the primaries than the general election. Primary elections are full of strategizing about how to pick a set of issues that will resonate with a large enough fraction of the electorate to be competitive, but which don't have other candidates campaigning on similar issues.
Too many candidates running on a similar set of issues will split the vote and will lose against a less popular candidate running alone on a different set of issues. So they end up needing to consolidate (which can involve some wheeling and dealing like promising that the candidate who steps down will get a position in the remaining candidate's administration).
This is essentially what happened in the 2016 Republican primaries. The more moderate candidates never consolidated and so split the vote among themselves. By the time they had seen the writing on the wall and dropped out, Trump had built up a large enough margin that the only remaining candidate (Cruz) had no chance at catching up.
RCV will likely prevent a similar outcome in the future. But a further consequence is that candidates will have less incentive to drop out early in the primaries. So if RCV were instituted nationwide I would expect the primary season to be longer, messier, and much more crowded.