yes, it is possible. Keeping two lighted bulbs adjacent.

Let's assume initial state of circuit as {0,0,0,1,1,0,0,0,0.....,0,0}

where 1 = Switched ON nd 0 = Switched OFF

choose second last bulb from bulb which has state =1, then 2 bulb will be lighted on either sides

next state becomes {1,0,1,1,1,1,0,1,0,0,0.....0,0}

so at each step we are lighting 4 bulbs, since 2012 is multiple of 4, there will come a stage where all bulbs will be ON.