Light switch setup using only white wire. Will it work?
Aside from being a code violation of outrageous proportions, if this is 120VAC you would have the delightful condition that the light sockets were always hot/live - this can make changing a lightbulb into a shocking experience, and under the right conditions, also your last.

You may also get some interesting magnetic effects from the loop wiring. 

Don't do this. The only level it "works" at is the Dr. Frankenstein's Laboratory level, and most people are not as tough as Igor. If it's actually something you found (or even, nay, especially, if it's something you are responsible for creating), rip it the heck out and do it right.