Yes!! You are talking about using two alternating blocks. So many "patterns" are made up of two alternating blocks which then give a "secondary" pattern and a much different look.
the pattern Omigosh is a great example of combining two traditional quilt blocks into a completely different "secondary" pattern. One of them is the Nine patch.
I have an ap on my iPad which allows me to combine two different quilt blocks in a quilt to see what the secondary pattern will look like. It's great fun!!