You can ;)
There was even such a case when a chatbot on Twitter learned to speak positively about Hitler.
But immediately after that, the chatbot was turned off.
Well, in fact, there has already been a similar incident: Microsoft launched a teenage bot on twitter, which had to be disabled within a day. The fact is that the bot has learned to speak uncivilizedly under the influence of provocative questions from other users.
More details can be found here: https://geektimes.ru/post/273276/
It depends on what you mean by bad, because a neural network is not a full-fledged intelligence or intelligence and it will not go to kill people with a cleverly thought-out plan.
But it can do what it was taught or what it learned itself if the architecture provides for unsupervised learning. Therefore, it is quite possible to teach her to do something "bad"