I run 17 inch wheels on my A4 that has 345mm TRW brakes very similar to what you have. That brake system is designated a 17 inch design.
I believe the S3 has slightly smaller 340mm discs so shouldn't be a problem and as the photo above proves is doable.
Certainly if you go aftermarket the clearance between the caliper and wheel is usually better.
I know it's not an S3 but my winter wheels are the standard 17 inch SE alloys, Balance weights are close but they work fine.
With the normal 17 inch summer wheels I run there is loads of room
@C2 DTN we have a full set of brand new winter wheels and tyres at work that are heavily discounted. They're for a mk3 TT, but if 17's fit over S3 brakes as they seem to in a post above, then these wheels will fit on your S3. Drop me a text tomorrow and I'll email you the specs. Off the top of my head they would be £2k + if someone walked in and ordered them.
I'm just going to run my current wheels over winter but stick winter tyres on them. I think I saw conti's on black circles for £106 a corner? Seems fair to me as they should last me 2/3 winters (depending on how many empty car parks I can find when it does snow