If an asteroid is heading towards the Earth from behind the Sun, will we be able to detect it?
Of course! We can use space probes and orbiting and ground-based telescopes.
Unidentified NEOs (Near Earth Objects) or PHOs (Potentially Hazardous Objects) are unidentified because they absorb so much sunlight (they are so dark) or so far away that instruments on earth and on space probes can't detect the light reflecting off the surfaces of these objects. So you could say they are invisible.
Now your scenario means that the asteroid will indefinitely be illuminated by Sunlight as it passes behind the sun - relative to our perspective that is. So instruments will easily detect this asteroid.
For an example look at this image taken by SOHO
Courtesy NASA http://www.nasa.gov/sites/default/files/thumbnails/image/soho_c3_comet
See how easy it is to make out this comet. So It will take no time to detect. What we should be worried about it how to prepare for it as it may cause biblical like catastrophies.