Yes you can move up your departure day by one day (or any number of days) in order to rebook for fewer points. As already stated, be sure you use the "Change" option, do NOT cancel and rebook. EBCI is tied to your confirmation number and that stays the same if you change your flights. If you cancel and rebook, you get a new confirmation number and your EBCI will be lost.
As to whether it impacts your place in the EBCI queue, at one time there was some evidence that it did. I'm not sure that is still the case. On our last trip I did reprice our flights at least once and we still got great boarding positions.