Sorry, but no.
3D object textures are not even seamlessly transferable between equally capable 3D rendering programs, so a drag and drop solution to your question is not going to happen. However, basic textures (and I imagine Photoshop is only creating the most basic of basic) can pretty easily be set up to work properly if you know where to look and what the textures do. Photoshop most likely created a color (commonly referred to as a "diffuse") map, and either a bump map or normal map, possibly both. The easiest and fastest way to work with .obj's within AE is by using Video Copilot's plugin "Element 3D". It allows you to import the .obj file and provides channels for you to place your texture maps in their respective places. Beyond the placement of your diffuse and bump/normal maps, you will need to play around with settings for specular (basically surface light reflectance), glossiness, reflection (the mirror kind) and you will likely need to click a checkbox that says "show backfaces", since by default, Element only renders the front facing side of a polygon (the surface "normal"). You can do all these things in C4D as well, with a much greater amount of control, but if you are unfamiliar with the interface and the endless texturing options of C4D, it'll likely be more difficult than you are hoping for. C4D is also considerably slower to render than Element, though it can produce much higher quality results depending on your needs.