Yes, verification helps posts reach a wider audience, but the way it works is more indirect than many people realize, it's not like the algorithm sees the badge and automatically boosts your content; that doesn't happen, what does happen is that people trust verified profiles more, and that changes their behavior.
Platform data shows that verified members experience a significant increase in profile views and engagement on their posts, they also receive more connection requests, but this isn't magic, it's because verification makes you appear more credible and professional, the badge gives you an initial boost of trust, when someone receives your request or views your profile, the verified checkmark tells them you're a real person, not a fake profile, this makes them more likely to accept requests, expanding your network, with more connections, more people see your content, and the algorithm then says, this is interesting, and shows it to more people, but remember, relevant content and consistency are still the main drivers, verification is an accelerator, without good content, it won't work miracles.