It doesn't appear so as it's not mentioned in the Swift API v1.0 docs http://developer.openstack.org/api-re...

The API documentation is not complete, so you should verify this directly by checking in the configuration file.

Add object version /etc/swift/container-server/container-server.conf

To enable object versioning, the cloud provider sets the allow_versions option to TRUE in the container configuration file.

This feature has been in Swift since at least 2012, so there is a good chance it is in v1.

If the question is about Swift releases, the 1.0 did not support object versions. The first release that did was 1.5.0, committed in June 2012. It was part of OpenStack Essex release.