I kinda like this idea - after all, a true adc without mana would make for an interesting, if not infuriating, lane phase - but the trouble would be making it balanced. Even champions that are considered lane bullies by nature - Caitlyn is a prime example that comes to mind - has mana issues to make sure she doesn't just spam her peacemaker or snap traps.
If I may be allowed to make an example of a true manaless ADC - without extras like energy or rage - I have a slight concept that could work out.
Instead of having a strict damage output ADC, we add some little bits of Urgot and Kennen in there. We have them remain without any resource but have it so they have some way to shred armor, gain some tankiness, and have CC. They would be reliant on extended fights of course and they would also have to be squishier and have less overall damage compared to other ADCs of course, but imagine being able to have a support that functions as your carry. Lets say their passive is that they shred X amount of armor to a single target up to X amount per AA. That would not only work great for removing tanks, but also lane bullying an ADC or bothersome tanky support (( looking at you, Leona )). And then how about for one of their abilities they could have some way to CC without having it as their ult or a trap that deals damage? Just a flat snare - not a stun or knockup, holy crap that'd be OP considering a person couldn't even fight back - that can help with ganks, keep someone from escaping under tower, or just flat out removing them from a teamfight.
An ADC of this nature would rely both on their autos because of a passive like in the example, have the utility to help in team fights, and not need mana or any resource to worry about.
On the downsides of using one of this nature, they wouldn't have any major late game most likely - after all, a lot of utility and lane bullying can have a price cough Miss fortune cough - they would be slightly squishier, and would almost require a support like Sona, Bruam, or Soraka to keep them alive during lane phase.
Maybe I'm just being dumb. :P < Anyone else think this might work or is this just silliness I typed?