From FM12 with FM11 editor data: yes, editor data from previous version works with the new. The problem is not incimpatibility, it is that the new version may have added teams that the editor had to add the previous and so there's duplicates in leagues that then turn to get over the stated team limit, things like that.
So, you should be able to play FM13 with FM12 databases (that contain only changes to make from the game's), but you need the luck that changes between 13 and 12 don't cause such issues. If, when FM13 editor is released, you load the old version you can check what is making it not work. Some times just loading and saving does the trick (that's true even within patches to the same version).
That's how I hope to be able to release my Complete Spain database within the week of release *fingers crossed*. The database for FM12 I made, I made by loading the FM11 database on the FM12 editor and then going through promotions/relegations and removing duplicated teams in Tercera.