A couple of decades ago Dr. Victor McKusick suggested that Abraham Lincoln may have had Marfan's syndrome and that the museum's specimens should be tested. I'm going by memory here, but I think a blue-ribbon committee was convened, debated, and a decision was made not to test the material because the science wasn't advanced enough yet, and it didn't really matter if Lincoln had Marfan's. Read the three NY Times articles linked above rather than trust my memory. McKusik died recently and the Washington Post ran an obituary and an appreciation while the NY Times ran an obituary.
At the moment, the museum is not contemplating DNA tests on Lincoln's remains, nor any other individuals.