After reading this topic, and some similar ones on the internet, I tried to test my own camera (a T5i) to see if there's any difference between normal viewfinder shooting, viewfinder + mirror lockup, and finally live view. Tripod, 10 seconds timer, stabilizer off, manual settings. Couldn't find a single difference between the three photos.
The thing is, you could manually enable/disable EFCS on old Canon models - on newer ones, it's always enabled and you can't turn it off. However, the bigger culprit is that Rebels use a single motor for both mirror and shutter, so the mirror always flips before taking a photo no matter what.