Can I add/install overhead kitchen cabinets without a wall?
Adding a wall beside an island seems a major step backwards from current trends of open and airy interior architecture, which have been steadily embraced for decades.  The obvious solution would be to add a drop down wall, or even just suspend cabinets from the ceiling, like this:
.
(found here).

One idea to help integrate that into the kitchen would be to add beams over the rest of the room:


To do this right requires cutting some holes into the ceiling, tying bracing into the ceiling joists, and then repairing the ceiling.  This is a medium sized job for a competent contractor, costing anywhere from $500 to $3000 depending on the scale and specifics of your house.  As a do-it-yourself, it is perhaps $50 in materials plus the cabinets and 20 to 60 hours of effort, most of which is drywall work to match the rest of the ceiling.