Can wearing a hat everyday 1 month after a hair transplant affect future growth?

If you wear hat, it should not effect future hair growth, unless you wear a very tight hat right after hair transplant that causes the follicles to come out. 

If you are comfortable wearing a hat after a hair transplant, do so. I, in fact, give patients a hat when they leave our office to keep their confidentiality intact and hair transplant their own business