Of course, they can arrest you even if you don't talk to them. It's ultimately up them whether to arrest you, not to you. You don't necessarily get out of getting arrested by not talking to them. (If they say you can get out of getting arrested by talking to them, they can be lying!). But you make it much worse by talking to them.
I spoke to a family friend who quit the police department I was dealing with over ethical concerns. He said that it was pretty standard practice, especially when dealing with a case they had zero suspects on. He said, "they'll bring you in, they'll tell you you failed, and they'll tell you that if you confess, they'll go easy on you because you're so young. It's not the results that matter on a polygraph, it's the answers you give. Don't lie, and don't incriminate yourself."
He was 100% correct. They brought me back to the station, into an interrogation room, and after about an hour of waiting, told me exactly what he said they would.
I lost all respect for law enforcement through that process.