Will making 1,000 hard links bog down an old CPU?

No, that number of links should be a tiny CPU task. The system creates directory entries and updates filesystem metadata; it does not copy the files’ contents. A slow drive or busy filesystem could make the operation take a little longer, but CPU load should be negligible.

The bigger question is whether you need 1,000 file links at all. A hard link is another name for the same file, so changes through either name affect the same underlying data, and removing one name does not remove the data while another link remains. Hard links also generally have to stay on the same filesystem.

If you just want another path to the whole folder, a symbolic link to the directory is usually simpler. Adding or removing files in the original folder will show up through that link too. Ordinary hard links to directories are generally not allowed.

For a thousand, I wouldn't worry about the processor. Each link is a small filesystem operation, though a separate command for every file can add needless overhead. If you are following a backup or deduplication scheme, check that it specifically calls for hard links, since they are useful when separate file names should refer to unchanged shared data.