Is it feasible? Yes; everything I've seen tells me this is not just feasible but relatively straightforward. It's just a matter of getting the pieces to talk to each other in a way that's friendly to the user.
Those last four words are the killer. Unless this becomes as easy to set up as creating a Facebook account, it will be a distant also-ran.
That is, I fear, where this project will meet its biggest resistance: the indifference of the nontechnical user.
I run this site with Movable Type, which as much as I love it sports several major drawbacks. One is that it is moderately hard to install and rather tough to upgrade. It's not a push-button process. WordPress has a major advantage in this regard: once you set it up, it's almost totally self-maintaining.
Diaspora* must be at least this easy to use, if not easier. That right there is project enough to give people months of sleepless nights.
From what few hints are available on the project's site, they are planning to do this — to make the process of setting up a Disapora* node as straightforward as installing a program on your own computer. The bad news is, I don't see how this is possible without either a) the end user having intimate knowledge of web hosting (something even many WP users don't have, to say nothing of Facebook users), or b) the Diaspora* people working closely with a number of web-hosting outfits to make this happen ... which means people would have to pay for their own hosting, a major downside right there.
A parallel to this question was brought up in a Q&A on their own blog:
What is the strategy to get to a critical mass of users (or avoid having to get a critical mass?)
We think that there is a solid contingent of people who would want to host their own node. How many people host their own blog? That’s not certainly Facebook numbers, but once we get that first kernel of people using it, we think people will see that having (at least) a copy of your data which you can apply to anything is a really empowering proposition, and not just in a social networking context.
Once again I cannot help but see what I would call the Nerd Myopia Effect here. It's too easy to assume that the word will be spread by people "like you" to "just plain folks", when most of the people who would host their own node are not automatically going to be in the business of evangelizing that, with all of the attendant headache that implies. Facebook is free and dead easy to get going with, and for most people — loss of privacy aside — that's the big attraction.
The problem I see is not technological, but social. People have, for a long time now, had the choice of paying for a degree of control (run your own blog) vs. trading some privacy for having many free goodies (Facebook). Even many of my fellow geeks are not interested in paying for many things on the web; why do it when there's a perfectly suitable, if crippled, free alternative? My feeling is that if people get fed up and ditch Facebook, odds are most of them will not replace it with anything; they're going to go back to a life that's mainly lived offline — which is where most of them were before all this goofiness got started, anyway.
So what would work? One approach I can think of is what Flickr did. A re-hosting service (or one of many) could get into the business of helping you set up your Diaspora* account, initially free but perhaps with cost-plus advantages. The restrictions on the free accounts are tuned so as not to alienate users too quickly, and the costs are reasonable enough (and perhaps scaled according to needed features/bandwidth/storage).
The problem, of course, is whether or not that simply puts us right back to where we started. That the code for Diaspora* will be freely available is slim compensation.
In short, I wish them a ton of luck — and once there's something resembling a usable piece of code, I plan on giving it a whirl. I don't have much of an investment in Facebook except in the sense that everyone else uses it. But that right there is the point of it, isn't it?