Surely, the point of base training is not to fly a circuit, but to ensure the student can fly an adequate final approach, flare and touchdown. Therefore, it would seem to me that conditions on finals, and whether the visual cues for the flare can be met would dictate whether is is suitable for base training.
I have done base training off short pattern ILS when the cloud base was 700ft but the vis and conditions below were good - it took a lot longer!!
Again, after base training and jet training for 30 years. It's up to the trainer if he can fulfill the requirements of the exercise.