It would be quite possible to design a processor that is not designed around series of instructions at all, but something more akin to functional programming. In this case, everything will “actually happen” without any kind of series of instructions.
Maybe my imagination isn't strong enough, but I don't see how a processor could work without being reducible to a series of instructions. The lowest level of "code" you give it might be more "functional", but there's a direct mapping between that and a sequence of states the processor goes through to actually do anything.
