Cool pic. It can be done safely on a carbon bike! Here's Chris Horner giving a guy (and his bike) a lift a few years ago. He had been flushed out the back after working for someone else in a race and picked up this guy who'd flatted. Gave him a ride up the rest of the climb.
Chris Horner Gives Fallen Rider (and bike) a 2k Ride to the Finish | Swift
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N = '96 Colnago C40, '04 Wilier Alpe D'Huez, '10 Colnago EPS, '85 Merckx Pro, '89 Merckx Century, '86 Tommasini Professional, '04 Teschner Aero FX Pro, '05 Alan Carbon Cross, '86 De Rosa Professional, '95 Gios Compact Pro, '95 Carrera Zeus, ‘81 Masi Gran Criterium, ‘81 Merckx Pro, ‘89 Cinelli Supercorsa, ‘83 Bianchi Specialissima, ‘VO Randonneur, Ritchey Breakaway Steel, Rivendell Rambouillet, Heron Randonneur, ‘92 Ciöcc Columbus EL