If an Edo character opened all Inner Gates, I don't think he would be able to keep the 8th Gate open forever, but I don't think he would die after using it. This could be advantageous, kind of like Madara dropping meteors on himself, because the body would recover from the technique, and theoretically, the user would be able to do it again.
However, the rules for Edo Tensei are constantly changing. For instance, the only way to eliminate an Edo person was to seal them. However, after the war started, the person could resolve any lingering regrets and be released automatically. Then, Madara was able to release himself by knowing the seals. Another rule that has changed is directly related to Edo regeneration. Originally, the body would recover from anything. However, there have been at least two cases when this didn't happen. Edo Itachi lost the use of his eye after using Izanami, and Obito was able to transplant new eyes onto the dead Jinchuriki. This doesn't really make sense, since their bodies should have immediately rejected the eyes and regenerated their original ones.
Perhaps, techniques that require some sort of known sacrifice, like Izanami, Izanagi, and opening the Eight Inner Gates, all require the sacrifice, even if the person is an Edo. This would mean that opening the Eight Inner Gates would pretty much be sacrificing one of your indestructible soldiers.
