A course in art history is great the same way reading Shakespeare and the Bible is great when you decided to delve into literature: it gives you a foundation on which to base your understanding of modern photography, since so much of what we do now references what has already been done. You also learn about a rich language of symbology, about emotional expression and a lot of color theory.
Painting is photography's close cousin and it has been influencing photography since photography was invented (and, lately, the other way around as well). Paintings are, in a sense, purer than photographs because everything they contain is placed there on purpose. The composition, lighting, aspect, subject matter... everything is there because someone took the time to paint it there. Painters work with multiple planes, they don't have hacks like shallow DOF. Happy accidents are very rare, and that's a great thing to learn from.
Do all these things translate to photography directly? No, you can't recreate Picasso's Nude Woman with a Necklace, but you can take a lesson from his use of color and positioning. You can learn poses, you can learn so much about light and expression. A painting like The Blue Boy would work just as well as a photograph, don't you think?
As to resources... this is a pretty decent book, but generally speaking, any album with paintings that you enjoy would be a great starting-off point. You don't need to buy it, scour your local library. I have a personal fondness for the old Dutch masters, if only because of their "photorealistic" approach to light.