In the scenario as played out on the video I believe from ML TWR it would have been possible to keep azimuth throughout the incident. As the 27 go around went through the intersection (from which the video is shot) the RWY 34 aircraft would be to the ADC's front and right and the 27 aircraft would be to his left and moving behind to the left. Might it have looked close out the window? I wasn't there so couldn't say.
Is there a point where if both aircraft went around they could conceivably reach the intersection at the same time and same altitude. I suppose so. I have no doubt ATC would have a plan of action if that was looking like it was going to be the case. I'd like to think the aircrew would as well given they are all told about each other.