Yes: it is the same subject, treated in a novel. Pirandello wrote One, No One, and One Hundred Thousand between 1916 and 1926, in the same years as his great theatrical period, and Six Characters in Search of an Author premiered in 1921. In both, the question is that of human identity: who we are.
Pirandello's whole work, in the theater, the novel and the short stories, revolves around a single problem, that of human identity. In the play, the Father puts forward the thesis that each of us believes himself to be one, which is not true, because there are many, as many as the possibilities of being that exist in us. This is exactly what Moscarda shows in Book III, with the five fools in a single Moscarda, and when the reader sends away the old friend and, without knowing it, himself.
The play has another idea that the novel carries to the end. A character has a life of his own, fixed like a stone, and can ask a man who he is; the man, on the contrary, may be no one. This is the "no one" of the title. Moscarda is the man who may be no one: the figures others give him, the usurer, the Gengè, the madman, the penitent, work as fixed characters, and he fits none of them.
The difference lies in the middle. In the novel, the narrator is the very man who comes undone, and he speaks to the reader while coming undone. Another Pirandello novel on the subject, The Late Mattia Pascal, puts a man to inventing another name and failing, because no one lives without papers, without a past and without a family; Moscarda, on the contrary, discovers that he was never one.