A more precise answer to the question is yes.
avast does keep a copy of old versions, but they don't make them available for download (at least not to the public).
If you want a old(er) version, you will need to search for it.
If I have software I like, I always store a copy (full installer of course) on a storage medium.
I know for sure know that I even have a copy of version 4.x laying around here somewhere