No, there are not backward compatible and will not. To add to that, they are electrically incompatible with each other.
On the contrast there is a chance, LGA 775 socket motherboards (most) support both DDR2 and DDR3 memory. They have DDR2 and DDR3 slots and the user can select what kinda memory he requires. But they cannot be installed simultaneously. Eg. P5G41C-M LX