Can I have create an InnoDB table without a PK? If so, would a secondary index be used as the clustered index?
If you have a unique key that is not null, it gets promoted internally to be the clustered key (or if you have more than one that matches this criteria - the first one does.)

If you don't have a unique key that is not null, a hidden key is created that is 6 bytes in length.

There is no way to specify the key to cluster around, and there is no way to not have a clustered index.