The short answer
Yes. The barbell weight always counts in the total lifted weight.
The physics explanation
When you lift a barbell, your body applies force against the combined mass of the bar and the plates. Newton's second law (F = ma) does not distinguish between the steel of the bar and the steel of the plates. The bar contributes to the resistance, so it belongs in your training log.
Common reasons lifters ask this
Reason 1: Plate-centric thinking
Many lifters focus on the plates because those are the pieces they add and remove. It is easy to forget that the empty bar already weighs 20 kg or 45 lb.
Reason 2: Gym slang
When someone says "I squat 315," they mean 315 lb total — bar plus plates. When someone says "two plates," they mean two 45 lb plates per side, which is 225 lb total.
Reason 3: Comparing with machines
Selectorized machines do not have a separate bar weight, which can create confusion when transitioning to free barbell work.
What happens if you ignore the bar
If you log only the plates, every lift will be off by 20 kg or 45 lb. Over time, that error compounds and makes your training history inaccurate.