Can a portable swamp cooler be hooked into a central air duct and recirculate?
Where they work, swamp coolers work because evaporating water cools the air being pulled in (via latent heat of vaporization - go visit a chemistry site if that's a concept you haven't gotten in your education.) 

Making the air humid does not, in itself make it cool - at a given temperature, humid air feels warmer to people, as sweat evaporates poorly. Starting from hot dry air, the swamp cooler makes cool, moist air. Starting from warm moist air, it just blows warm moist air around.

So, if you recirculate swamp-cooler air, the air in your house becomes increasingly humid, with two effects - one is that it evaporates less water at the swamp cooler, and thus is cooled less, and the other is that the internal air becomes more humid. In the long term, it will be more uncomfortable in the house than out, as house temperature will rise to outside temperature, but be more humid.