It should work, but you will need to check and make sure that the 3.6 style has all of the new images from the 3.7 style. Copy any of the missing images from a default 3.7 version and paste them in the 3.6 folder.
You may have to update the CSS file if it looks messed up in certain areas of your AdminCP.
If it's one of my 3.6 styles let me know and I'll make it availible for 3.7 and 3.8...