Heck no. Any high school student who has had a first aid class knows that.
ETA: You can actually kill someone if you start doing chest compressions on them if they have a beating heart by interrupting their rhythm.
http://heart.arizona.edu/frequently-asked-questions
perform CPR while it is beating?
The physicians and scientists at the Sarver Heart Center, have found that the old saying "Never perform CPR on beating heart" is not valid. According to these professionals, the chances that a bystander could harm a person by pressing on their chest are slim to none, even if the heart is working normally. Therefore, they recommend following the "Better safe than sorry" approach and begin chest compressions. It is better to perform a few unnecessary chest compressions for someone with a beating heart, rather than withhold chest compressions and circulation from someone in cardiac arrest.
Why don’t you check for a pulse?
We do NOT recommend that lay public rescuers waste time trying to assess for a palpable pulse. During Dr. Kern’s tenure as AHA National ACLS Chairman, the AHA came to the same conclusion. Public lay rescuers cannot reliably detect the absence of a pulse in a timely fashion, hence in the 2000 and 2005 AHA CPR Guidelines (Circulation 2005; 112(24): IV-3), this requirement was removed.
Studies have also shown that even if a person manages to locate the correct spot for detecting a pulse, there is a high chance that the pulse they may detect is their own, especially considering heightened stress levels in such situations. Rather than wasting time trying to detect a pulse that may or may not be the victim's own pulse, it is better to get perfusion to the brain by continuous chest compressions.
The correct response to a witnessed cardiac arrest is to:
Check for responsiveness (shake and shout).
IF NO RESPONSE, call for help ("911") or ask someone else to call.
Begin uninterrupted forceful continuous chest compressions immediately.
Call for an AED if one is nearby and available.