Yes, you can purchase a music license for a video you've already uploaded to YouTube, as long as the video is still 'Unlisted'.
If your video has already been uploaded as 'Private' or 'Public' then you cannot purchase a license retrospectively.
Purchasing a license for an 'unlisted' won't stop you from initially receiving a YouTube copyright claim. This is because our VOUCH software cannot automatically release claims on a video ID retroactively.
Follow our steps here to contact our team to get your claim(s) removed