No, they don't. If both are on the same side of the grommet your battery can't send current through the coil to heat it up and make tasty vapor.
DISCLAIMER: I think I understand basic circuits well enough, but I'm still new to vaping. Please do speak/post up if there's something incorrect in my explanation below!
Remember, current flows in a closed loop. We want current to flow in a path from the positive side of the battery, through the coil, and then back to the negative side of the battery. When current flows through the length of resistance wire wound up into a coil, the wire heats up enough vaporize e-liquid.
The idea on these heads is that one leg of the coil (one lead/side) goes outside the pin grommet and the other leg goes inside. The intact grommet acts as an electrical insulator; current shouldn't flow through that grommet. The grommet and center pin also provide physical pressure to keep each leg pressed against the metal piece to which it's meant to connect.
The negative side will be the leg/lead of the coil outside the grommet. This leg on the outside connects to the frame of the cup, ...
which in turn connects to the body of your tank through the threads where the head screws into the base, ...
which in turn connects to the negative side of your battery through the threads where your tank screws onto the battery/mod.
The positive side will be the leg/lead of the coil inside the grommet. This leg gets connected to the little metal center pin when you push that inside the grommet from the bottom. The tip/head of that center metal pin connects to the center post, either directly to the post on your battery for eGo-threaded devices or indirectly through the insulated structure at the base of a tank using the smaller 510 threads. That inside, center pin of your battery/mod is the positive side of your battery. It's sometimes on a spring that will give a bit under pressure, and the ones I've seen often look to be made of a metal with more of a yellow tint than the metal on the rest of the device.
Putting both legs/leads on the same side of the grommet would defeat the purpose, no matter what kind of coil(s) you built inside the head.
Now, for this specific case of a vertical coil, you want the leg coming off the top of the coil to be outside the grommet and the leg coming off the bottom of the coil to be inside the grommet. Remember that the body of the core, the cup, is going to be connected to the negative side of your battery. The leg coming off the top of the vertical coil is going to have a lot more physical space where it could touch the cup, so set that one up to be the negative lead anyway. The leg coming off the bottom of the vertical coil has a shorter and straighter path down towards the center of the intended arrangement, so it's better suited to be the positive lead closest to center.
I hope this helps. I don't like being told what to do without at least being given the opportunity to understand why I'm doing it that way, so I have trouble writing instructions without including the reasoning. (No, fans of TL;DR don't often enjoy my style, but by now they're not reading anymore anyway. Neener neener!)
Cheers & Good luck!
