Yes, the English sentence is idiomatic. I imagine padding around to be moving around gently, softly, as though not wearing shoes, just on the 'pads' of the feet. I notice two of the OED's example sentences involve people in socks .
a. intransitive. Of a person: to walk with soft, steady steps, esp. without shoes, etc., putting each foot down quietly in a single motion. Of an animal: to walk softly, stealthily, or calmly. Also with the feet as subject.
1837 M. M. Sherwood Henry Milner iii. ii Footsteps were heard padding along.
1871 G. MacDonald Love's Ordeal xxiii A hound, Padding with gentle paws upon the road.
1926 A. Bennett Ld. Raingo i. ii. 7 A nice thing, that with five servants in the place, and him a millionaire, he should be reduced to padding about in his socks!
1975 M. Bradbury Hist. Man vii. 126 Felicity pads at Howard's side down the long bright passage.
1997 S. Grafton M is for Malice iv. 53 I padded down the stairs in my sock feet.