No. Sure, it was supposed to have this purpose, to literally stigmatize Hester fas an adulteress. But from the very beginning, Hester does a symbolic act of embroidering the letter so it looks beautiful. If she has to wear it, she will wear it in her own way, under her conditions. Just like all other people, Hester has to accept what is given to her. But she isn't just a passive recipient. She is an active doer who changes things for herself. So, the letter gains various other symbolic layers throughout the novel. Stern and austere people that surround Hester eventually start thinking that the letter stands for "able".
