Does it work when a defendant tries to excuse away crimes by saying he was abused as a child?

No. In fact, it can work against him:

We tested a novel theoretical model explaining the psychological processes underlying jurorsâ discussions about a defendantâs history of child abuse and alcohol abuse in a capital case. We coded the extent to which jurors used child abuse and alcohol abuse as mitigating factors, as aggravating factors, or argued that they should be ignored. Relying on attribution theory, we coded the extent to which jurors rendered controllable or uncontrollable and stable or unstable attributions regarding the defendantâs history of child abuse and alcohol abuse. Jurors were more likely to argue that child abuse and alcohol abuse should not be used as mitigators or to even use them against the defendant as aggravators than they were to use them as mitigators. Jurors made more controllable than uncontrollable attributions regarding child abuse and more stable than unstable attributions regarding both child abuse and alcohol abuse. The more jurors supported the death penalty, the more they argued to discount child abuse and alcohol abuse as mitigators or use them as aggravators and the more controllable and stable attributions they made. Political orientation predicted discussions and attributions about alcohol abuse, but not child abuse.

Source: “Jurorsâ discussions of a defendantâs history of child abuse and alcohol abuse in capital sentencing deliberations.” from Psychology, Public Policy, and Law