Well, I believe calibre moves each file it controls, but mostly should be done pretty fast -- on modern filesystems.
External storage meant for switching between OSes still needs FAT, which requires making copies of all files
very slow.
(same problem renaming dozens of authors/titles.)
calibre doesn't rename files, it hardlinks/copies them (depending on filesystem support for hardlinks) and then expires the old copies.
Like theducks, I prefer to let the OS handle what it is good at handling, no need to get calibre involved...