It really just depends. The cross-reactivity shown in the lab was outside the body and may not accurately represent a significant response in natural situations. Lab experiments are helpful tools, but more work would be needed to establish what the actual effect would be in the real world.
Macrophages and neutrophils would already be fighting SARS-CoV-2 virions in any healthy person. If some T cells join the fight, that's going to be helpful. The question the remains is: to what extent? Perhaps it's enough to completely halt infections in their tracks. Unlikely, given the lack of significant numbers of T cells and the lack of coordinated B cell lymphocyte action, but who knows. Maybe it reduces the severity of infection as you suggested. That's certainly possible. It may also be that actual cross-reactivity in the body is minimal and the T cells aren't even that involved.
The difficulty here is that challenge trials are unethical and the pool of SARS2003 survivors is so tiny that you'd have a hard time studying this any other way. It's interesting data, and with luck we'll see some useful long-lasting immune system reaction with COVID-19. So far, those who were previously infected with SARS-CoV-2 appear to have great immunity moving forward. That's great news.
Very good points.
My suspicion is that Covid may be more like the common cold coronaviruses than we think:
*first infection is severe, except in kids where it is just a cold
*reinfection occurs every few years, but those later ones are mild.
The only difference with Covid is that it is new, so most of us never got that first infection in childhood.