I am not the expert on the process used. I assume that when a new UID case is added with DNA or DNA is added to an existing case, the DNA runs through the entire database and looks for a match. if it is found, great they got a match, if not then it remains in the UID files.
I assume when a new missing person is added with DNA the same process is run. however, the two main types of DNA are not interchangeable, i.e. the mitochondrial and the nuclear DNA. so unless you have mtDNA or nucDNA from both the UID and the MP, even if they are a match, it will not be picked up.