First, virtually no one is use the pre-Windows operating system called MS-DOS. I think you means the Windows version of InDesign installed with a version of Creative Suite.
Second, if it's a CS version InDesign, you cannot download and install the Mac version and use the serial number. You have to call Adobe Customer Support and ask to transfer your license between platforms.
(Note that if you were using the subscription model InDesign CC, you could install versions on both platforms.)
Thank you very much !