swimming with impingement syndrome

Yes, but not in swimming. I played through four years of volleyball-induced impingement syndrome in my right shoulder, and eventually had surgery on it. I was told that every swing I took was doing more damage. I assume that the same is now true of my left shoulder, which has chronic impingement issues and for which I'm considering getting surgery sometime in the next year (see my recent thread in this forum).

Take my advice with a grain of salt (or a few tablespoons of salt), because I've never done an IM, but I would take the recommended 2-3 weeks off swimming. Let your shoulder settle down. Ice, take NSAIDs, and ease back into training in a few weeks. If you keep swimming now, you'll continue doing damage to the tissues. If you let the inflammation go down, it's less likely that you'll be doing further damage when you go back to swimming. Yes, you'll lose a few weeks of training, but the earlier you give your shoulder a break, the less time it'll take to let your shoulder settle down. You don't want to be get into a situation where it's five weeks from race day and your shoulder is now so bad that you have to take the remaining five weeks off just to be able to race.

In the meantime, depending on your shoulder's anatomy and how you kick, kicking with a kickboard might actually aggravate it more. I kick on my back, without a kickboard, because my left shoulder's impingement is exacerbated by using a kickboard (even the kind of board that's supposed to be easier on the shoulders). YMMV.