I am wondering if ICE has the legal authority to immediately deport illegal immigrants after they have received medical care at U.S. hospitals for COVID-19. I am referring to people who voluntarily came into U.S. hospitals to receive this medical treatment.
How do you define "immediately"? ICE can certainly arrest them. Many of them will need to be placed in removal proceedings before an immigration judge before they can be removed.
Moreover, if ICE does have the legal authority to do this, do the mayors of sanctuary cities currently have a legal right to intervene to stop ICE from deporting these particular illegal immigrants? I am thinking in particular about the mayors of cities throughout the state of California.
In general, of course not. No state or local official has the authority to prevent a federal officer from making a lawful arrest.
There may be provisions to delay the arrest, for example while the intended subject of the arrest is hospitalized, but people who have recovered from COVID-19 (or any other disease) would be subject to arrest if ICE can get their hands on them.
Sanctuary cities are not obliged to help ICE identify, locate, or arrest people, but to the extent that ICE can do that by itself, sanctuary cities cannot impede it.