eh I think they would. Izanagi can alter reality right? What's to stop the user from altering reality to one in which they never got caught by the reaper death seal? Although I guess it depends on how the "soul" and chakra are related. If chakra and the soul are the same thing then while your soul is being pulled out, you would have no ability to use jutsu. However, if I recall Orochimaru was able to move his sword through the third hokage while the third was pulling out his soul, without touching the sword. This makes me think that you can still manipulate chakra and use jutsu even while your soul is being pulled out, therefore you could still use Izanagi.