No. All defendants in first-degree murder cases get a sentencing hearing regardless of whether they were convicted at trial or pleaded guilty (or no contest). It is during the penalty hearing that the jury determines whether or not to impose death or prison. Note that sometimes defendants agree to a plea bargain where they plead guilty to first-degree murder in exchange for the prosecution's promise not to seek the death penalty. This way the defendant avoids death, and the prosecution avoids having to put on a trial.