It definitely depends on the tank and the type of fish. Also, it depends on what you have on the tank and in the tank for filtration. If you have a top-notch filtration system (large amounts of flow, no dead zones, excellent skimmer, an abundance of live rock), one dead fish will barely cause an ammonia spike. If you have a new tank where all of the levels are unstable already though, you will want to try and get it out before it begins to decompose.
You said that you were having multiple deaths, and if this was the case, then I would definitely try and get them out. One death is okay, multiple would be a problem because either there is a problem with the tank that is causing them to die one by one, or else the ammonia spike that the first death caused is beginning to kill others.