I guess it could. I usually use the mug to soak my brush in hot water before using it. If you just use the tap to do it, I guess it would! =) It also depends on if you lather on the face or in the mug/bowl.
If you lather on your face and only do 1-pass, i.e. do not relather then this is fine alone. If you re-lather then a mug sitting in hot water in your sink will keep your brush and ambient lather warm which makes a huge difference in the quality of your shave. I'm personally not a bit advocate of lathering in a mug/bowl but obviously if someone is they would need that as well.