Disable proximity sensor when locked

If my phone is sitting on my desk locked, something like a napkin is just covering the proximity sensor, and I get a notification or something, the screen will not turn on. Can this be disabled?

Short answer

No, this is not possible with a standard installation of iOS.

Long answer

Yes, this is possible if your iPhone happens to be jailbroken. If so you can install software that allows you to create custom gestures. This is achieved through the installation of a couple of packages: Always on Proximity and Activator.

NOTE: This answer in no way supports or endorses jailbreaking your device.