Yes and no or to be precise - to a certain degree but not through an exposed language feature.
PostgreSQL still does copy-on-write so the old versions of the row exist and are present in storage. However now there is an autovacuum process going over the records regularly marking those no longer seen by any transactions as re-usable so eventually the old records would get overwritten.
You can get at the older versions of the rows directly on disk or perhaps it would be possible to get the db to return such older versions of the rows. It seems that by default even trying to get at them with `ctid` is not possible so that may require hacking PostgreSQL itself or using some extension which seem to actually exist[1].
[1] - https://github.com/omniti-labs/pgtreats/tree/master/contrib/...