I think most people underestimate how much of their immune system depends on their sleep. Sleep quality, amount (hours) of sleep, time in bed, all of it -- they matter.

In stressful periods, it's likely not stress crushing the immune system, it's the indirect relationship that stress causes bad quality sleep and low amount of sleep, that in turn crushes the immune system.

If, even if under stress, you manage to work out a system/habit that allows you to get proper sleep, you'd likely be ok.