App permissions allow the app to use certain aspects of the phone. For example, if an app has camera permissions, then it can use the camera.
As for your question, potentially yes, if the developer coded for that. An app can use the camera without your knowledge to take pictures IF the developer was a crook and hid that code in the app. It's up to you if you would trust the developer not to do that. Are they actually doing it? If the app was downloaded from a legitimate source, not likeky. Google does do regular inspections of the apps in the app store and removes apps that violate these stuff. They are also able to send commands to your phones through the play store app to remove the app that was found to be malware.
But the app having those permissions does not mean it does that. It just means that it has the potential to do that. But there are also certain combinations of permissions that need for this to happen. For example an app with camera permissions but no permission for interner access, this is no danger. Because even if it can use the camera without your knowledge, it has no permission to use internet to send those pictures it took anywhere.
Other apps are made actually to do that for specific purposes. For example a security app like Cerberus was specifically designed to take a picture with the front camera and send and email with that picture if someone entered the wrong passcode on your phone, and this is designed to happen without the person entering the wrong code that it happened.
Basically, don't get anything outside of legitimate sources and you should be relatively safe.
But that does not mean it doesn't happen.