Nothing much.The 'Hawaiian' Republic is very much just an oligarchy controlled by white-American businessmen backed by the US military against native revolts.The US would still have use of it's various military installations regardless of whether it was annexed or not.Only difference may be better treatment of the natives if the natives are made US citizens with an annexation--instead,the US currently get the excuse of not interfering with the apartheid regime because it's not really US territory.