Maybe a little bit
A body that is very fatigued, due to lack of sleep
, excess stress
, being overworked, etc.
.. May get sick more easily. If a person improves and returns to a normal type and duration of sleep, he will no longer have a "lack of sleep". His body and immune system will become more "normal", so his chances of getting sick will be similar to that of a healthy person. Sleeping even more hours won't help.