Yes, I've done this a few times over the last 5 or 6 years In fact, I just did it a minute ago and it worked as expected. I did the following steps:
1. Navigated to the /Applications/Utilities folder and double clicked the "Adobe AIR Uninstaller"
2. Accepted the dialog that told me that AIR 24 was going to be uninstalled (and showed me what applications would be affected)
3. Once the uninstall was done, I navigated to the AIR Archive page and downloaded an old version of AIR (v16 to be exact) - Find and download archived versions of Adobe AIR SDK
4. Ran the installer and installed AIR 16
What version are you trying to install? Is there a reason why you need the old version?