How important is Grand Admiral Thrawn to the Empire? From another point of view, how significant would his death be to the galaxy? What kind of response will that elicit from the Emperor?
The Emporer sees everyone who is not the Emporer as expendable. Maul, Dooku, Vader are all just tools to help build and maintain his power. In the same way that Ships and Storm troopers are.
Thrawn is the same. He may be useful, but if he died the Emporer would not feel sad.
Depends what literature you read.
Thrawn states one of the reasons he was sent to the Outer Rim was because he is an Alien and the Emperor disliked and never trusted non humans seeing them largely as being beneath him hence his reaching the office of Grand Admiral was an even bigger achievement
However he was also considered to be the greatest tactical Mind of the Empire and that is how he reached his position.
Now the interesting question is whether Thrawn exists in the current version of the Starwars Universe. Yes he appeared in the extended universe and therefore is now confined to being alternate history. However his first ever appearance was in the Lucas Arts game Tie Fighter (one of the greatest space sims ever made) as this as the Lucas Label on it does this make it Cannon to the current universe?