Would Nature, Science or other leading academic journals prioritize publishing work on COVID-19, the novel coronavirus that has caused more than 3k deaths so far? If so, has this happened before in the past, during another crisis?
Absolutely. Journals are ways of disseminating scientific information, and they do take into account what is of current interest.
More specifically, however: Both Science and Nature do not just publish scientific articles, but also commentary and news stories. For example, in Science they are in the "News" and "Perspectives" parts of the magazine, and they definitely cover current events. As, if I may add, they should.
When your question bears the underlying motive/question, if it easier to publish in nature and science in the next years by doing research on this topic, then my answer would be no. There will likely be an over-proportional amount of COVID-19 related papers be published in top-tier magazines, but at the same time an enormous amount of additional funding money will flow into biomedical research institutes and create competition to solve this problem in a kind of competition, while many biometdical researchers and drug developers have already stated that the development of a remedy against COVID-19 will take 1-2 years. As Buffy commented above and I conclude, the review likely becomes and should much more rigorous for COVID-19 related papers. Additionally the submission rate and competition to get into review will rise.
I'm aware of several retractions in nature magazine covering biomedical breakthroughs over the past years. Many retractions related to COVID-19 would not be very advertising for a journal within a reproduction crisis within academia.
I also want to mention that really important and technical papers are not only published in top-tier journals like nature and science, often the authors also choose intentionally a journal within the community to fasten the progress and reach the biggest possible dissemination. In case of COVID-19 a journal most of the researchers within a community have access to and which offers a format allowing the authors to transport the content they think is necessary to disseminate in the fastest and most completest way with short review time (which is often much longer among nature and science) to the community is probably a much better choice to save human lives.
It's a delicate question when the research question affects million of lives within a short time period, what ethically the right publishing and reviewing behaviour should be amoung authors and journals. There are of course preprints for nature and science, but do nature and science really have the best specialists, reviewers and review system for solving a very specific scientific problem within short time or rather journals that cover since decades virus deseases? I'm at least wondering if COVID-19 will also create new ways of publishing/commenting of researchers worldwide within short-time on a very high quality level and with open-source access.
So I'm skeptical about @Wolfgang Bangerth's answer if Nature and Science should prioritize COVID-19 papers without changing their review system/duration and if both magazines are the best place to publish such papers concerning the importance of a fast progress in R&D. This depends really a lot upon how biomedical researchers share information in the fastest way via specific journals with short but rigorous review while retaining a high reproduction rate of the results.