"Remaining Story Points" field for individual Stories

Is it possible to add such a field, and have Burndown Charts use that value?

Or is this a violation of "how Scrum works"?

Related to this is logging of work. Normally you log work in time units. But we would like to log work as "story points worth of work". Basically, we're after the same functionality for Story Points as we already have for time (Estimate, Spent, Remaining).