Okay, here's my experience, though not scientific. I don't have a site that has Expertise, Authority or Trust as it relates to the medical field, so I have no E.A.T. credibility as it relates to the current pandemic.
I wrote a blog post relating the virus to my industry. Nothing serious, more of a humorous story about the lengths some people are going to during the pandemic. Definitely nothing that I would want to preempt serious medical content.
Most of the content I normally write, takes about a week before it starts getting organic hits. GSC also typically takes 7-10 days before it shows an increase in the number valid pages (under Coverage), which I've always interpreted to mean "Google has finally indexed my page".
The blog post I wrote started showing up in Google Analytics within a few hours, but GSC still hadn't shown an increase in the valid page count. When I used GSC to evaluate what queries users were using that Google displayed my page for, the queries were a broad mix but related to what Google thought were keywords in my blog post.
I'll keep this updated as time progresses and if I see anything different.
April 4 update. I've posted 3 or 4 blog posts around current issue with COVID-19 and CARES Act. Each of them has been picked up by Google within 24 hours. I.e., users coming from Google. I know that doesn't prove that Google places a priority for urgency, but it's obviously aware of current trends and news.