You won't get anywhere if you are rude, bossy and don't contribute anything useful when you post comments.
If you went to a cocktail party in your new city, the first words out of your mouth would not be about what you are selling. You would introduce yourself, listen to what others have to say and get into the conversation only when you have something useful or interesting to contribute.
You start an interaction, and before long you have people who like you. You then have a following of people who realise that you know what you are talking about and you are someone who also reciprocates and takes an interest in what they have to say.
Remember that being social is a two-way street. After a while you become known as an expert in your field and only then should you slowly introduce your followers to your product. By then they will trust you, like you and buy.
Facebook is a huge virtual city of people, all with needs and desires and looking for information, so seek the right people out and they then become your targeted audience.
This whole scenario comes under the heading of attraction marketing, and it works both offline and online.
So yes, Facebook marketing does work if you are patient and go about it the right way.