Not always. If something "goes both ways" or "works both ways," it means that the relationship is reciprocal, but not always in a good way. It could mean that each side can harm or exploit the other, or that the same rules apply to both sides.
Another idiom for cooperation is "you scratch my back and I'll scratch yours" or "one hand washes the other."
Knowing what you are trying to communicate, I can see the meaning. However, if I heard someone say "The road goes both ways," I would think they were saying something along the lines of: You have to take the good with the bad. It is similar to "cuts both ways." So, I would probably recommend rewording it.
The feeling goes both ways. I think this is closer to what you were intending, but it is still a bit awkward sounding.
The feeling is mutual. This is the most common way to communicate the sentiment you are after--that I can think of, at least.