My personal experience to-date suggests that good IT (i.e. IT that is designed, implemented and used well) offers the competing results you speak of — an initial decrease in the need for bureaucrats and increased opportunities for other data-related bureaucratic activities.

In practice, I have seen two other phenomena that both work to increase bureaucratic staff numbers:

a) IT tends to make work practices quite rigid. There is one way of doing things and that is the way coded into the system. This certainly gives the dramatic efficiency gains that you speak of, but is often ill-suited to the vagaries of changing requirements. I have seen so many cobbled-together work-arounds for so many systems in my life that I couldn’t begin to count them. I have also spoken to (and worked with) many, many bureaucrats whose professional lives ride on those work-arounds.

b) IT projects, at least in the public sphere, are rarely implemented (or, frankly, designed) well. This seems to exacerbate the problem in point (a).

I don’t mean to dismiss the power of IT in reducing bureaucratic overhead. My professional life up until taking on economics was all about using IT for exactly that purpose. I’m just not sure how we might identify when it would actually decrease the number of bureaucrats and when it would simply increase the volume of output from the bureaucracy without increasing the amount of “true” work achieved or decreasing the staff levels.