Diabetes is covered in the compulsory insurance. They will probably reject your application for supplementary though...
Can I suggest you read through the thread here completely, and contact Jenny - I can highly recommend her.
We are finding the system excellent...
Not everything on this thread, though, is true...
You have to pay and are covered by the compulsory insurance technically from the day you arrive. You have three months to set things up but if you *are* covered from the day you arrive, and you *do* have to backpay...sometimes the date can be fudged, or is taken from the 1st of the month you arrive - my experience is that using an insurance broker (Jenny) was worth it.
Your compulsory health insurance can cost less than 250chf a month...the price does vary a bit. It's not any more expensive if you have diabetes - this is the *wonderful* thing about the system - compulsory is the same, covers the same stuff for everyone...
Also, it depends if your employer covers your accident/sickness insurance - so for example my insurance is higher than my husbands because I am not working so my premium includes my accident/sickness, whereas he doesn't need it because his employer pays for it...
I'll PM you about the diabetes info...