Well, it's better not to argue about words ... but I would say, that it makes more sense not to consider the photoelectric effect as ionisation. (There is no ion produced anyway, is there? :))
There is nothing special about charges in metals (and there is also nothing special about the slow free electron produced), and nothing "bad", whereas ionising radiation is associated with bad things like cancer etc.
The electron was not tightly bound to an atom anyway, there are plenty of those free electrons in the metal, and you can move them and thansfer them to other pieces of metal with simple electrical fields. The effect has much more in common with heating the metal than with ionisation. You do something to a big reservoire of electrons, not to a single atom.
My conclusion: one can definitely argue which radiation is potentially ionising (see comments to the question), but clearly this very process is not an ionization.