Could I mix blackberry compote into german buttercream for frosting in between cake layers?

It depends on how liquidy the compote is. If it's thick, like a jam or preserve, it should be fine. If it's runny, I would cook it down slowly until it thickens to jam consistency. The other option--if the cake layers are a bit dry, like a genoise--is to brush the compote directly onto the cake layer, as long as it won't get too soggy. I would use just a few Tbs (just like you might brush a cake layer with espresso or rum...). Then add the frosting on top.
I love the flavor profile--let us know how it turns out!