Not likey. Just make a copy of it and try.
[Moved to Elements forum.]
It might work, but there might be problems. PrE 11 & 12 were a fairly major departure from earlier versions.
Ideally, I would finish the Project in PrE 9, if at all possible. If not possible, I would try to Open that PrE 9 PREL (the Project file) in PrE 12, but expect some issues - maybe not enough to worry about.
As Peru Bob pointed out, work from a copy of the Premiere Elements 9.0/9.0.1 project.prel instead of the original.