Yes, but the re-download option only works if you've already downloaded that specific OS version in the past. You must have at one point in time downloaded that specific version of Mac OS to your Mac via the App Store. Otherwise, you're forever locked out from downloading it ever- permanently. And, only the latest version is available.
So, if you happened to forget to download it or maybe skipped it, then Apple doesn't allow you to download it again- ever. Some customers may have very specific reasons for not being able to run the latest version of Mac OS X. Or, they don't update their machines for a reason. Or, they may have a need to download and run an earlier version of Mac OS X that -is- still supported for their hardware, but just not the latest version. And, what Apple has done is basically made it very difficult.
Back in the pre-Mac OS X days, Apple made their entire OS library officially available in many different places on the internet- ie official Apple's web site, Apple's FTP sites, Apple's Hotline server (for those who remember those) etc etc. And, customers knew that non-supported OS versions are "non-supported," and that's fine... But, everything is so strict now. It's not as friendly and easy as before...