No, you will not increase your baldness. You may lose hair during a fast, but it will regrow. Now, everyone does not lose hair while fasting, so you may not.
Male pattern baldness is attributed to Dihydroxytestosterone or DHT. After you finish your fast and refeeding, you want to take some supplements to control and get rid off DHT.
Zinc, Saw Palmetto, Ashwagandha, Rhodiola, Pumpkin seed oil, vitamin B5 and Biotin will help with balding.
However, fasting will help balance your hormones, which may help your baldness.