On the implausibility of offering the cock gold wings and a silver comb (or some such thing), it has occurred to me that maybe the woman doesn't even mean what she is saying. Could it not be possible that she is simply offering it something valuable off the top of her head because she is desperate to keep it from crowing? She doesn't necessarily think it will hear her or accept the offering, or even that she can hold true to her promise. The offer of gold and silver is simply a commonplace way of showing her desperation. I don't think that ballads have to reflect real life in every detail. Rather, it is the questions they make us ask or the values they contain which are important.
But, having said this, the Roman connection is still very interesting to think about and I don't think the two, or more, interpretations are mutually exclusive.