Hi Lisa - look, I'll give this a go. And these are my personal views and experiences.
Mission critical parts to us would mean that it would likely be called a Significant Service Contract here in New Zealand. Right now, with a greater focus on broader / social outcomes in place across many organisations, internal culture might indeed get a rating, or be evident in measures about environmental outputs, staff training or recruitment.
That said, you'd expect for mission critical parts that the greatest weighting would be their ability to deliver, and depending on the total weightings, it's probably likely that a company that can show this better, even with a lesser internal culture, would be likely to end up chosen in a supplier relationship.
Yes, at least to the extent that 'culture' reflects underlying honesty and integrity. If something is mission critical, it is essential that the supplier is reliable. It is also important that they do not represent a reputational risk, especially if transfer to an alternative supplier would be difficult or take time to achieve.