Not really positive of the answer, but I would think so.
The three wire between switches red & black are travelers, meaning only one of the two are hot depending on the position of the switches. The hot is on either the red or black, and the neutral is constant.
If you are not getting a tone, it would have to be that you are not getting power through the switch on the end where your hotwire comes into the switchbox. I would suspect off the top of my head that you have a bad switch. If you need me to explain how a 3-way works, I'd be happy to try.
(don't really know how much you know about them)
Hope this helps
Ken F