This is such an interesting question and It think its worth orgs thinking through their approach prior to it happening.
Currently we do not ask if they have applied and been denied - I can see value in that… and there is a little bit of an “ignorance is bliss” to not asking.
To me, the facts and circumstances would really matter - were they denied because they simply filled something out wrong and/or were unresponsive to some request for clarification OR were they denied because the IRS really determined their mission was not charitable. If deemed to be not charitable, does that seem like a clerical error or misunderstanding of their mission or were they really operating in a bit of the gray area.
If we knew they had been denied I would think we would need to dive deep into understanding why they were denied (if known), what they may have adjusted in response to the denial, and possibly loop in legal support to make our own determination on the Charitability of their work. If they were denied because the IRS deemed their work not-charitable, I would find it very hard to look past that and take on the project. It Feels very risky to form a new internal charitable program knowing the IRS has already said it is not charitable.