No it could be an emergent property that arises from physical processes but is not reducible to them (emergentism). It could be that the mental and the physical are not independent substances but different elements of the same thing, and thus one does not need to be reducible to the other (neutral monism). Or you could be a dualist and claim that the mind really is separate from the physical world.
Or, more sensibly, you could be agnostic because we lack any solid grounds for belief in any theory of the mind.
And again, as I just said, this ontological problem is separate from the phenomenological problem with which the existentialists were concerned. For what the mind is, ontologically, makes no difference to our subjective experience as radically free beings without a predetermined essence.