Not natively, as far as I'm aware.
It might be possible to build something along these lines, using the API, but I can see plenty of difficulties with doing that.
I'm more thinking; why would you want to limit a user, in that way? - if your concern is over impact on key business operations, then shorter time intervals of monitoring are much more important.
Taking your own number as an example, 1 GB is only around 90 Kbps, so that usage is very unlikely to affect your business applications, unless it all occurs in a short time interval. I would have thought that limiting clients or bandwidth-hungry & non-business appliactions to a specific traffic celing would be a much better way of ensuring bandwidth is best used.