Question: There are reports that men with beards may have problems using face masks effectively or getting hooked up to a ventilator correctly. Given the danger posed by the COVID-19 virus, should Jewish men shave their beards before they fall ill?

Answer: 
Anesthesiologist here: Beards aren't a problem for a ventilator.
They make my job harder when I have to mask ventilate someone before putting in a breathing tube, but since we've stopped mask ventilating covid-19 patients, it doesn't matter.

A beard will make it impossible for a traditional N95 respirator to fit properly, which will preclude you from protecting yourself (or other people) from breathing in the virus.

A year ago, I'd recommend buying a PAPR (Powered Air Purifying Respirator) which is the space hood you've seen, and which works just as well as an N95 but would let you keep the beard. Now that you can't find one available to buy, if you want to wear an N95 respirator mask properly, trim the beard.

Health care facilities fit test all employees yearly to make sure we can wear N95 respirator masks properly.

I have colleagues who have trimmed beards because, while in years past we could avoid having them work with patients with things like tuberculosis, this year, everyone is at risk of covid-19.

(This doesn't answer the question, but does clarify that a beard isn't a problem at all for being on a ventilator. The goal, of course, is to avoid needing the ventilator in the first place...)
This question is "consult your Rabbi" question.
That being said, 

During six-days war, soldiers were asked to shave their beards so gas-masks will fit better.
[Rabbi Shlomo Goren](https://www.inn.co.il/News/News.aspx/336825) resisted that ,and it was concluded that every soldier will decide for himself.

(EDIT: He resisted because he thought that damage of demoralization is grater then the risk of possible gas attack)

I also found [somebody](https://www.bhol.co.il/forums/topic.asp?cat_id=4&topic_id=2902705&forum_id=771) who says that during the gulf wars many people and rabbis shaved their beards, also hinted by Rabbi Yona Mtzger [here](https://www.srugim.co.il/10803-%D7%94%D7%A8%D7%91-%D7%9E%D7%A6%D7%92%D7%A8-%D7%9C%D7%A9%D7%A8-%D7%94%D7%91%D7%99%D7%98%D7%97%D7%95%D7%9F-%D7%93%D7%90%D7%92-%D7%9C%D7%9E%D7%A1%D7%9B%D7%95%D7%AA-%D7%90%D7%91%D7%9B-%D7%9C%D7%91).