No, if your posts are public. X says accounts you block can still see public posts, although they cannot like, reply to or repost them. Blocking someone is therefore not a way to hide an old public post from that account.
Choose the action by what you want to change
To stop that account directly engaging with you, blocking still has a role: it prevents following, Direct Messages and engagement with your posts. It also removes the follow relationship if you were following each other.
To limit who can read your posts on X, review protected-post settings. X says blocked accounts cannot see protected posts. Protecting also limits access to earlier public posts, while making the account public again exposes previously protected posts.
To remove a particular post from your account, review and delete that post. If you want to keep a personal copy, save it before removal. Blocking an account does not perform that cleanup for you.
Review and delete your old X posts
Copies need their own check
Protected posts can still be captured and shared by followers. Deleting a post also does not remove text someone has copied into a separate post or content held on another website. Check the actual copy you are concerned about, rather than assuming a privacy change reaches it.
X: what happens when you delete a post
If the original is gone but a Google result remains, use the separate search-result guide. It explains how an outdated result differs from a copy that is still available.
Why does a deleted social post still appear in Google?
For old replies, check the account audience
A reply can feel like a conversation with one person, but that does not establish who can read it. Check whether the account posting it is public or protected before deciding that blocking has dealt with the concern.