Yes, you can. From New PicMonkey just click on your name in upper right drop down to switch back. 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encourage you to "switch" to New PicMonkey and get to know the new features and expanded platform as Old PicMonkey is no longer updated.
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.