No, he didn't write like him. Dead Souls is much better than Poor Folk, a rather forgettable early effort by the master. Dostoevsky's later works (Crime & Punishment, The Idiot, Brothers Karamazov, etc) are where he really excelled as an author.
Have you ever heard of Dmitry Merezhkovsky? If you like Russian literature, Death of the Gods is definitely worth seeking out. I read it years ago but I want to read it again:https://en.wikipedia.org/wiki/The_Death_of_the_Gods