I think they would. Suppose you extract the transplantable organs of a dead patient without permission, is it ethical? Have you harmed the patient? If the relatives don't find out, are they harmed?
Spain (and many other countries) decided that they would rather be opt-out, so by default you've consented. This is actually a great example of the power of defaults to affect an outcome. Because of this out-out, the number of donations increases significantly.
I'd be more interested to know what happens to foreigners. I suspect that they aren't treated as consenting, but I don't know.