Heck yeah! That should be fine. You just don't want your backerboard to be too flexible. When you put your spackle on, if it is going to flex (when you pick it up, move it around), the spackle will crack. Not might crack. It will crack. You said your board is 2/8ths thick ( ). 1/4" should be just fine.
If you solidly attach the board to your picture frame, you should be just fine. You will probably want to attach your board to the picture frame with either wood glue, construction glue and/or small nails. Just don't split your frame if you nail into it.
Alright so on Wed thru Friday I will be gone on a school trip...we're going camping please don't ask why. Plus I am in Public school. Anyways I won't be on for 2 days I will be back early friday afternoon.