One run a week isn’t worth it.
Any running is better than no running.
It’s true that fitness and performance won’t improve much with a single weekly run. However, that single workout can provide a mental boost and keep you in the habit of exercising at least a little bit – which will make it easier to gradually add additional workouts when time allows.
Stay motivated by running with a friend on her easy day or with a group run for beginners – check your local running club for opportunities.