Yes, lack of sleep can affect your immune system. Studies show that people who don't get quality sleep or enough sleep are more likely to get sick after being exposed to a virus, such as a common cold virus. Lack of sleep can also affect how fast you recover if you do get sick.
During sleep, your immune system releases proteins called cytokines, some of which help promote sleep. Certain cytokines need to increase when you have an infection or inflammation, or when you're under stress. Sleep deprivation may decrease production of these protective cytokines. In addition, infection-fighting antibodies and cells are reduced during periods when you don't get enough sleep.
From the Mayo Clinic