That's one interpretation. Another is that he did kill people (and Paul Allen), but there's so much mistaken identity going on that few people actually know who is who. For example, note how some of his colleagues mistake who he (Patrick Bateman) is in the office "show me your card" scene. And also how Paul Allen has luch with Bateman thinking he is Halberstram. The novel is set up this way. It's supposed to be ambiguous.
Bateman was a non memorable person. The fact people mistaken him all the time shows that no matter how expensive his suits, how nice his business cards, how much he spends on glasses and 1000's of situps, he still can't stand out from the crowd he is in. They are all clones of each other. He was gifted his dad's company and is a spoiled child. He draws up these scenes as a way to stand out in his head. He so badly just wants to be noticed. At the end of the book when they scroll through his journal you can tell he is a sociopath. He admitted over and over that he is a killer and people just laugh at him. No one takes him serious. It was BEE way of showing how the wall street crowd think they are so special but are all just a subclass of humans.