It's certainly possible, depending on the quality level of the screen. Even "premium" screens could do this but you wouldn't expect to see so many screens unless you got a really bad batch.
The easiest way to test is to replace the battery with a Power Supply and note the current draw and how it compares between good and bad screens. A poor quality backlight could draw excessive current. Also, are you eliminating the FCAM/Sensor as a variable?