Can early stud death affect offspring?

Well, there are a number of things that can be genetic, but there are more things that are because of poor maintanance, diet, handling... could have contracted a disease from another animal. 16 years isn't long for a horse, let alone a QH, but there are many extra things to do for horses getting into their senior years that the owners perhaps just failed to do. There are not very many deadly genetic diseases I can think of off the top of my head, especially for QH's because they are usually so darn healthy and hardy. If you really really want to know then dig harder and find out how he died. Otherwise, enjoy your horsey =-)