The limited success I have had with WILD have been from the onset of sleep. So yes, it is possible.
It has to do with the mental frame of mind more so than the time or method.

Often WBTB method works very well with the WILD technique because your conscious mind has been more or less controlled by your subconscious sleeping mind.
So as you wake up and go back to bed your subconscious is still at an easily engaged state and your logical processes of your brain have been awoken enough to maintain control through the WILDing process but not too much to the point of waking yourself up.