Short answer: Linux kernel 4.4 does not have this bug. You should not run into it on Ubuntu 16.04 LTS.
If you follow the email chain that you linked, you'll get to this message by Nicolai Hähnle:
Kernels that contain commit 954605ca "drm/radeon: use common fence
implementation for fences, v4" are safe, older kernels require a
NULL-pointer check around the call to radeon_fence_ref.
Here is the commit he's talking about on kernel.org. For a more useful visual, here is the same commit on GitHub. On the GitHub page, if you expand the list of commit branch and tag labels, you can see that the commit is included in the tag for the 4.4 kernel (see image below), so you should be fine.
If you really want to be sure, you can probably boot a LiveCD or USB key running Ubuntu 16.04 LTS (currently still in the beta stage of its release cycle) to test it on your computer.
Edit: It may also be worth noting that Debian 8.3 is no longer the latest version, as Debian 8.4 was released on April 2, 2016. However, Debian 8.4 ships with a kernel where this is still not fixed (3.16.7-ckt25-1). It's important to note that the real thing to look for is not what Linux release you're using, but what kernel you're running. In your case (Debian), kernel 3.16.7-ckt25-1 has this problem while 3.16.7-ckt20-1+deb8u4 and 3.16.7-ckt26 do not (relevant bug report).
Edit 2: You can also, as fduff points out in this comment, install a different kernel version on your existing system. Though, I think that's a bit outside the scope of the question you posed, which was simply, "So if I install Ubuntu 16.04 LTS with Linux kernel kernel 4.4, I will not get this bug? Yes or no?"