They are currently designing a small, unmanned spacecraft based on the assumption that they could get this to work if they had enough antiprotons. The plan is not to make it to a star, but rather something more modest that will travel 10,000 A.U. in a 50 year flight. Their initial design parameters have a 100kg dry mass and 400kg of fuel. The alternate design, using DT pellets, burns all the fuel in only 0.1years and still makes it out to the same distance in the same time, but it needs 26 micrograms of antiprotons. It also relied on ion beams to compress much larger fuel pellets, instead of the electromagnetic trap design they presented at the conference, so I'm not sure it's comparable at all.
Less shielding is needed to protect the antiprotons themselves.
Anyway, I thought it was interesting. If anyone wants more info, that's really all I know, so I'm not the one to ask. I assume that with enough antiprotons, this scheme could be scaled up for an interstellar spaceship. If there was a better way to couple the fusion reaction into fewer, faster thrust particles, there would be a lot of room for improvement.