Not in the sense of "can't be opened without the key".
Good locks buy you two things: Deterrence (maybe), and a set minimum of time and noise requirements to bypass them. If your lock reputably takes 3 minutes to pick or a Ramset gun to blast them open, make sure your guard comes by every two minutes, and otherwise stays in earshot.
Also 3) intrusion detection.
It's obvious to the owner and the whole world that an intrusion has occurred if the door is sawed open or the lock is cut off. It's nice to know your home has been broken into vs. some of your jewelry is gone and you don't know whether to blame your teenager, a relative, someone who did work on your house since you last checked, etc.
Photos of your sawed open door will probably help in your insurance claim too. Telling your assessor "the cops say they might have picked the lock" isn't something I'd want to rely on to get my claim approved.