Yes - but why???
The answer to this question is yes. But if you have access to Black Powder, why dilute it with Pyrodex? Good Black Powder will ignite better than Pyrodex and is not any harder to clean. If you have a good source, it usually costs less too.
I know some folks have a hard time finding Black Powder in ther local area, and they load a few grains of black then Pyrodex over top. This gives a surer ignition. I did this for an experiment until I found a better supply of black powder.
JPM