The reason the C# compiler requires you to chain to the default constructor (i.e. append : this()
to your constructor declaration) when auto-implemented properties are used is because all variables need to be assigned before exiting the constructor. Now, auto-implemented properties mess this up a bit in that they don't allow you to directly access the variables that back the properties. The method the compiler uses to get around this is to automatically assign all the variables to their default values, and to insure this, you must chain to the default constructor. It's not a particularly clever method, but it does the job well enough.
So indeed, this will mean that some variables will end up getting initialised twice. However, I don't think this will be a big performance problem. I would be very surprised it the compiler (or at very least the JIT) didn't simply remove the first initialisation statement for any variable that is set twice in your constructor. A quick benchmark should confirm this for you, though I'm quite sure you will get the suspected results. (If you by chance don't, and you absolutely need the tiny performance boost that avoidance of duplicate initialisation offers, you can just define your properties the normal way, i.e. with backing variables.)
To be honest, my advice would be not even to bother with auto-implemented properties in structures. It's perfectly acceptable just to use public variables in lieu of them, and they offer no less functionality than auto-implemented properties. Classes are a different situation of course, but I really wouldn't hesitate to use public variables in structs. (Any complex properties can be defined normally, if you need them.)
Hope that helps.