Do the genes encoded by the nucleus for mitochondrial proteins have introns?
Nuclear genes for proteins destined for the mitochondrion can have
  introns…


…to the extent that other nuclear genes for that organism have introns.

For certain insects there is a database of such genes entitled MitoDrome, and if you click on D. melanogaster in the side panel on the home page of that site you get to a list of such genes for the eponymous fruit fly. You can inspect each one with the ‘view’ option, and the first few I looked at all had introns. Here is an example for one of the subunits of NADH-ubiquinone oxidoreductase, ND-18:



The subunits of this enzyme complex can be examined in other species, from which one can find that in Homo sapiens these nuclear genes also have introns. A related human gene is NDUFS4. Mutations in this gene have been described, at least one of which results in a genetic desease — Leigh syndrome. One of these mutations involves abberant splicing of the five exons of the gene (Lamont et al. Am J Med Genet Part A 173A:596–600).

The homologous gene in Saccharomyces cerevisiae, NDI1, does not have introns, like most other yeast genes.