Does Windows calculate CRCs to check every file operation?

Windows doesn't actually preform any redundancy on file transfers, this is a misnomer for the device driver accessing a bad sector block (see the SO question What, and where, is the NTFS CRC windows complains about? and this Microsoft KB article; NTFS does not store any kind of file checksums). If you receive this error on your computer, you should ensure your hard disk's integrity (and possibly invoke chkdsk with the /r flag).

Long story short, Windows does not verify any files after they are transferred. You can use another software tool like TeraCopy to verify data after moving/copying files.