I did it twice. Never pulled the final drive.
When I did it for the first time, I injected 400ml into the tube and it was never seen again. Even only 150ml would be enough to fill the entire final drive with grease... Since there is enough slope, it definitely runs down the transmission into the final drive and stays there till the grease gets thick.
This method is not elegant or the best one, since you can't control the actual condition of the transmission, but I'm pretty sure it works fine to prevent the splines from getting dry and rusty.