No there aren't any organisms with fully functional mitochondria which (the latter) do not retain the minigenome.
On whether it is theoretically possible to transfer all the mitochondrial genes to the nucleus:
Perhaps it is possible and mitochondria may work just like lysosomes and ER, but I think that the responses will be greatly delayed. At present there are no mathematical models that can provide a better understanding of that possibility. Nonetheless, some studies have shown that chloroplasts and mitochondria also have redox dependent gene regulation by which the expression of some components of the ETC is regulated by the redox state of the quinone. This helps in optimization of the ETC; if all genes were in the nucleus then this would not be possible. This pheonomenon is, however, better studied in chloroplasts. See this review.