Only if the damaged part is covered by the insurer, ie engine usually not, unless damaged by joyrider, then certainly can be.
My gf's car is a write off, was rear ended, damage was more than car value, that was 4 years ago keep forgetting to repair it, as so hard to notice, was listed as needing a new rear 1/4 on a 94 astra, + bumper etc, it's a tiny dent about 1/8" deep and 4" long, still pocketed the £525 for repair cost so not worried.
It was a cat d when I bought it, so suppose it is twice now!!
tabetha