Not really. Aperiodic tilings, while lacking symmetry in a strict sense, still tend to look quite regular and repetitive, and thus non-natural.[1] Aperiodicity alone doesn't guarantee the "natural" look, which is unsurprising because natural textures are not stitched together from tiles either.

[1] https://commons.wikimedia.org/wiki/File:Rhombus_Penrose_tili...