Of course, it can, but it's WAY, WAY easier to check for a 3 parts antivirus program, than reinstalling Windows. Just do as described in earlier posts... Only taking seconds. Try that first...
If there is any, remove it, and restart... Will Windows Defender open? If yes, you can use your time for other things than reinstalling Windows!!
Uninstalling any third part antivirus program, won't uninstall your cracked game...