Maybe he did and maybe he didn't, but what's the value of a completely speculative prediction?
Inspiration, apparently? According to wikipedia, Watson and Crick both credited Schrödinger's book (what is life) as a source of inspiration for their initial research.
Apart from the amusement that might be had in making it, you never know if further evidence might one day cast new light on it.
Where? What is Life is an astounding piece. It influenced Watson, Crick and other biologists, but didn't predict a double helix.
It's a wonderful book. I am proud to have a copy :)
Erwin Chargaff himself a chemist, knew very well the proportion of the bases in DNA since he'd discovered it but didn't put two and two together (Chargaff's ratio).