You definitely should not even try. Most likely it will corrupt and destroy the files.
The programming is very different between versions 10 and 15. Version 15 is by no means backward compatible to version 10!
In my book, I always recommend finishing a Premiere Elements project in the same version of the program you started it in.
in general older projects should open fine in PRE 15. One way to check if it works for your specific projects is to download the free Premiere Elements 15 trial version and open your PRE 10 projects. Please ensure that you once opened, you save to new project files as you may not be able to open PRE 15 projects in PRE 10. If it works and you like the new features, you can go ahead and serialize the software.
I know you are part of the Premiere Elements tech team, Aurobinda, but I very much disagree. Version 15 is going to corrupt a version 10 file. I've seen it happen many times with pre-version 11 project files. At the very least, there is buggy behavior when the file is opened in version 15.
But if Jeffrey wants to try it anyway, I'd very much recommend he make a copy of the original .prel file and keep it as a backup just in case.
I recently upgraded from Premiere Elements 9 to Premiere Elements 15. I had no problem importing the older projects into Elements 15. I did have to wait a little, though, while Elements 15 imported, converted, and loaded the workspace and all the project assets from the Elements 9 project. Hope this answers your question.
It may work for some users, but is it worth the risk of starting a project and just after a complicated edit have it act up and lose your work?
Or it could save just fine and then the next time you try to open it, it won't open.