It will work, but you will only be using the 1900 mHz band as you already know, if you reach a region where Cingular is runing on the 850 mHz band, you will not have any coverage, not good if you're travelling, also the 850 mHz band penetrates building better than the 1900 mHz so again you might have signal problems inside buildings as well.
A note on the 900 mHz band, despite the close number,
GSM 850 is not compatible with
GSM 900. A phone that only has
GSM 850 cannot work on a
GSM 900 network, nor vice-versa.