That depends on how the in-universe logic works. For example, from the Wikipedia description of the plot, it would appear that the death of the Omega mind knocked him back to the beginning of the loop to the point that the paradoxes would not happen. That is before the entire series of resets and loops. Additionally, since the Omega no longer exists, it cannot affect anything including those who would have the blood of the Alpha or Omega. From the way it sounds, his next death would not affect anything. Of course, the fact that they plan a sequel may mean that they will change the rules.
Edge of Tomorrow
As for whether or not Cage is still able to time loop with no Mimics
left on Earth, the post-Omega reset should be Cage’s last. It can be
assumed that without the Mimic collective around, Cage no longer has
the power to reset time. Still, he might want to ask for a blood
transfusion, just to be safe. Otherwise, Major Cage is now free to
debrief Vrataski on what actually happened – over a cup of coffee
(with three sugars).
In the original story All You Need Is Kill the hero must kill the heroine so that the nexus ((called the Omega in the movie) will be unable to reset time. This is done by handwaving.