I have a 2014 S3, Ultegra mech g/set, Rotor QRings (52-36 mid compact, so the ovalised version of the default chainset).
To answer the OP, it's perfectly capable of climbing. The bottom line is that it's a very stiff carbon frame that will do what you ask of it. I built my S3 to be the perfect 'do it all bike' and have done Coast to Coast in a Day (242km, 4500m. It was a total joy.
The standard build didn't suit me though...
If you're used to a compact 50-34 and climb severe gradients (>20%) the challenge might be the mid-compact chainset, but your LBS should swap it out for a compact if you so desire. As it happens I opted to keep the 52-36 with an 11-32 cassette (which required a long derailleur). This gave me more range because I do climb severe gradients and wanted the S3 to be a 'do it all' bike. (The 36-32 gearing is similar to a 34-30.)
If your climbs are not so severe, or you're a more powerful climber than me, then perhaps you'll go with an 11-30, or 11-28 and be fine. (And can keep the standard derailleur, which is more aesthetically pleasing.)
I kept the standard Cosmic Elite wheel & Mavic tyres for training. They're fine but a bit heavy. The standard bike is about 7.8kg, inc pedals, cages, etc. With my adjustments (chain rings, cassette, cheap pedals, etc) it was nearer 8kg.
Ouch. (Di2 would weigh more too.)
But you know...this is WW, right? So I also have Wheelsmith Aero 50 tubs and some Pete Matthews alloy wheels. With the lighter wheels and so on, it's more like 7.3kg, inc pedals, cages etc.
(I have a cunning plan to take it down further.)
But here's the thing; when I bought it I went around the shop weighing all the other candidate bikes; R3, SuperSix, etc. There really isn't anything to choose between them. The standard R3 was a bit lighter, but only a bit.
Funnily enough I had real buyer's remorse. It was slow. Twitchy. Tiring. Loved the way it looked, though, always.
And now, after 1000km with it, it's amazing. It's fast. Accurate. And I've got used to the QRings, so it's not tiring at all.
I was riding it in RideLondon last week, transfixed by the rain and spray curving around the aero downtube. (Should have been looking where I was going - probably contributed to my puncture-fest.)
So, yes, with some thought and adjustments to reflect your riding style and capabilities, it's a do it all bike. And it will climb anything that you can.