Effective focal length with crop sensor, and detail of image

I have in fact read the other threads, and I am still not clear on this topic.

For any given lens, say a 400mm EF or FX telephoto, I am shooting a subject in low light, for arguments sake lets say I am shooting an eye chart (the kind you read in the military to check your vision).

The distance of the subject is such that no manner of focus or camera settings or photoshop manipulation will make the bottom line of the chart readable. The 2nd and 3rd lines to the bottom are almost readable when shot with the 400mm lens on a full frame body.

Will using a crop sensor body with the 400mm lens (having the effective focal length of 600mm) actually allow me to have better detail in my final image, and make those unreadable lines appear readable?

For arguments sake the camera bodies and sensors are identical in every regard except the crop factor, and forgetting arguments about final photo print size, pixel size, depth of field, etc., and only worrying about the final ability of the camera system to resolve detail in written words at extreme distances...

Logic would dictate that the answer is no; otherwise why wouldn't they make 5x or 10x crop sensor cameras so people could take advantage of insane effective focal lengths from their lenses? However I am seeing both answers when I google this, and a lot of confusing explanations.

Thanks!