No, if it says black has a 45 % chance of winning, it also says white has a 55 % chance of winning. Thus it gets more points if white wins.
OGS already calculates the expected winning probability to decide how much a rating should increase or decrease after a game. It’s somewhere in the code at GitHub - online-go/goratings: This repository contains the (future) official rating and ranking system for online-go.com, as well as analysis code and data to develop that system and compare it to other reference systems..
But I don’t know whether that’s up to date.