How to set a wallpaper for apps in full screen (in Yosemite and higher)
It doesn't look like there's a safe way of doing this; looking at this Apple Support Discussion answer, I can still find the referenced background image in my Yosemite install at:

/System/Library/Frameworks/AppKit.framework/Versions/C/Resources/NSTexturedFullScreenBackgroundColor.png

Since this is buried in /System, it's highly unlikely there's .plist file/attribute you could change to point to an alternative background – so you would need to replace this image file with another to change the background. As you may or may not know, editing anything within the /System directory is tempting super-bad juju and very, very, very strongly discouraged by Apple and any IT people worth their salt.

Personally, I would recommend that if you really want a window background image in these apps that you instead configure each app to use the background image and dispense with the transparency (or submit a feature request to Apple and embrace the restriction in the meantime).