No. Premiere Elements doesn't allow for a legacy save.
I would agree with SG's generalization "No. Premiere Elements doesn't allow for a legacy save.".
Therefore in your case, you cannot open a saved/closed Premiere Elements 12 project in Premiere Elements 11.
However, there is an exception to that generalization. Not sure how and why it came about, but...if you create a project in Premiere Elements 10 Windows, save/close it, you can re-open it in Premiere Elements 8.0/8.0.1 Windows. Not sure how useful that trivia is, but I present it to whomever may ever find themselves in that situation between Premiere Elements programs. But, there is a precaution, watch out for what is happening when you do this with regard to Scratch Disks direction in 10 and 8.0/8.0.1.