My understanding of modern correspondence chess is that it's mostly a computer vs. computer slugfest. Everyone will be using computer assistance - in arenas where computers are "banned", there are many, many cheaters - and the winner is the one who feeds their computer better ideas (although they are very strong, computers still have blind spots where human input improves their play). Playing without computers is suicide. Even with it it's very time intensive if you want to win at the highest level, because chess is probably drawn with best play and humans operating a strong computer are so close to perfect that it's very hard to win.
Because so much of your time is spent working with your computer, and you won't have a computer in OTB play, you probably won't improve a lot by playing correspondence chess. However, you will learn a lot about openings, because opening preparation is where the biggest edge in correspondence chess comes from.
Quoting top US Correspondence Chess player Wolf Morrow:
DN: Many players of the past were correspondence chess players. I think also today it's quite important, for improving to practice correspondence chess. What's your opinion about this?
WM: It depends on what you want to get out of modern correspondence chess. For me, I found it's a great tool to learn new openings or get a better understanding of main lines. As a result of my CC games, I'm more familiar with the Sicilian Sveshnikov than I would have ever learned as a passing interest in say a chess book or video on the subject. I've also heard and actually seen for myself that top OTB GMs will often use winning approaches taken directly from correspondence games, and then they get all the credit for coming up with this 'brilliant' new novelty to win the game. As I said, I've seen this happen on more than one occasion, and I say to myself "Uhh, no. He didn't invent that move, it was played 3 years ago on ICCF and we CC players are quite familiar with it".