That adaptor would only work with that motherboard. For the adaptor to work, the motherboard chipset would need to support both memory types which isn't a standard feature. It's also unlikely that anyone will make one for DDR2/DDR3 given that RAM isn't so expensive anymore and given the age of DDR3 (coming towards the end of it's lifecycle by the looks of it) it doesn't seem like many people would have need for it.
There are two reasons that you cannot use DDR4 in DDR3 or in the reverse order. One, the motherboard chipset doesn't support both memory types and two, they have different keys so one won't even fit into the others socket. There are some rumours that when Skylake is released next year that it will support DDR3 and DDR4.
As for using a testing adaptor, not all motherboards are compatible with them and i'm not sure if there are any performance penalties when they do work.