Yes, you can until the end of 2020 when this version will no longer be supported.
From New PicMonkey just click on your name in upper right drop down to switch back. You will need to reenable Flash in order for Old PicMonkey to work.
However, we encourage you to "switch" to New PicMonkey and get to know the new features and expanded platform as Old PicMonkey is no longer updated and will be supported after December 2020.
Read more: Why Do I Need to Switch to New PicMonkey?
Note: If you start a new design in New PicMonkey and then try to open it in Old PicMonkey, it will only be accessible as a flattened file.
However, if you open a file created in Old PicMonkey in New PicMonkey, it will still be multi-layered.