Wow - 1k in a day is really BIG miles
IMHO it would only be possible if you stay on the peage / autostradas as you will need to maintain a fairly hefty speed. Even averaging 100 m.p.h you will need 10 straight hours so it will be a long day in the saddle.
I don't think the riding position on the SS is that much more radical than an ST. My partner in crime on my trips used to ride a 916 and now has an Aprilia RSV Mille R Haga Replica and he reckons they are fine!
In theory it's a goer as long as you stick to the plan: stop only when you need petrol, eat and drink a little every stop, don't get side tracked. I have to say I don't think I would try it without some build up practice. Half my annual mileage every year is done on one trip and I try to get a couple of 200 mile + runs in before it. Even so I'm always knackered after the first day on any trip.
Having said that I am a fat old git with diabetes and arthritis so maybe that is the deciding factor
If you do go for it let me know as I'm thinking of going to Brno next year