Doing such an experiment on humans would obviously be unethical in the present circumstances. There has been a report that monkeys who recovered and were later re-infected with mega-doses of the Covid-19 virus didn't get sick again. This is not terribly conclusive, because monkeys don't get severe symptoms from SARS like we do, for example. (SARS is the closest relevant relative to the Covid-19 virus aka SARS-CoV-2.)
Immunity to a pathogen, in general takes about 3-4 weeks to develop to develop fully, so if you [get] re-infect[ed] with a larger dose within this window, even a after a vaccine, you can cause/get the disease, although it's apparently a pretty rare occurrence.
These individuals were likely resusceptible to reinfection with the same strain of influenza virus due to a confluence of unusual events. First, all three were reinfected within three weeks, before their primary adaptive response had sufficiently matured. Another contributing factor was the high level of circulation of the pandemic strain. [...]
Could reinfection also occur after immunization with influenza vaccine? Yes, if the immunized individual encounters the virus before the primary antibody response matures, which occurs in 3-4 weeks. This is more likely to occur during pandemic influenza when circulation of the virus is more extensive than in non-pandemic years.
Perez CM, Ferres M, & Labarca JA (2010). Pandemic (H1N1) 2009 Reinfection, Chile. Emerging infectious diseases, 16 (1), 156-7 PMID: 20031070
About the Fangcang-style hospitals (i.e. make-shift hospitals for those with mild or asymptomatic infections), which China says it closed the last one on March 10 (after there were 13 opened in Wuhan at the peak); it turns out they used now in other countries, and they are even a WHO recommendation of sorts (as of March 17):
WHO recommends that all laboratory confirmed cases be isolated and cared for in a health care facility.
If all mild cases cannot be isolated in health facilities, then those with mild illness and no risk factors may need to be isolated in non-traditional facilities, such as repurposed hotels, stadiums or gymnasiums where they can remain until their symptoms resolve and laboratory tests for COVID-19 virus are negative.
According to the (April 2) Lancet paper on Fangcang hospitals, they Chinese took various precautions to prevent cross-infection with other diseases in such settings. How strictly these measures have been implemented and how well replicated in non-Chines Fangcangs elsewhere, I won't venture to comment here, but CNN had a somewhat disparaging article about Fangcang hospitals back in February, outlining their shortcomings. Since then, the US has been arranging similarly looking facilities in the NY area, but I don't know how they intend to use them.