This sounds like a wonderful program. I'd like to draw on a wonderful experience as a graduate student involved in a digital project (redschoolhouse.org, with the UVA Writing Program and with some contact with the Scholar's Lab) in responding to the question.
I think, and I imagine you'd agree, that a "bad" version of such an internship would be to stick a grad student in a room to do some XML or whatever kind of markup for a whole summer, with no "big picture" benefits from participating in the program. I think what I gained in "big picture" terms from working on a project for a year was: 1) learning how programmers think and 2) learning how project managers think. Learning how project managers work is fairly easy to do, since one just needs to sit in on a lot of meetings to get the idea—but the benefit is that organizing a project from scratch at another institution would be much easier to do.
Thinking like a programmer has a steeper learning curve for most humanities grad students. I know a lot of DHers who generally "hack"—figuring out through trial and error some rudiments of CSS or PHP—and that's fine for limited and local problems, but it in no way amounts to expertise. But it seems like graduate students would be in a good position to learn some basic principles of programming (where to write subroutines, stacks, loops, etc.) and best practices, like documenting code and version control. These skills, while, granted, still well below the BS level in computer science, would aid these graduate students in doing better-informed "hacking" and explaining computer concepts to others, as well as in the future when they'll be working with full-on programmers to put their own projects into motion.
I'd be excited to see an internship that involved some workshops or independent learning about programming, such that new knowledge might be put to use while participating hands-on in ongoing projects.
