After the first few pages of signatories, I recognize very few of the names, so my guess is that LW signers will just get drowned in the much larger population of people who support the basic content of the research priorities document, which means there's not much downside to lots of LWers signing the open letter.
The Future of Life Institute has published their document Research priorities for robust and beneficial artificial intelligence and written an open letter for people to sign indicating their support.