Question: What I want to know is if it is possible for two planets to be close enough together to tidally lock each other (as in both planets are tidally locked), but in such a manner that they don't orbit each other. More specifically, could this happen in such a manner that the one further from their star would be perpetually in the shadow of the other?

I know, weirdly specific question. I'd be interested in the reasoning/science behind the answer, but a simple yes/no answer would actually suffice. (in case anyone's wondering, backstory for two a WH40k Wolf successor armies).

Answer: 
Yes, but only for a few moments or hours before they crash into each other.

In the absence of a mutual orbit, there is no force to prevent their mutual gravitational attraction from pulling them into each other, and this will happen very quickly.
If the two planets are close to the same size, it would be possible to give them each a relative velocity such that neither is technically orbiting the other, but rather both are orbiting a point in space between the two. Such an orbit could easily be stable as long as there aren't too many other large bodies passing by, and the planets would tend to become tidally locked to each other over time. To my knowledge, we haven't seen any planets arranged like this yet, but there are binary star systems with such a configuration.

With a bit of juggling of the math, and the mass of the star and the planets you could probably find a point where the orbital period of the two planets around their common point matched the orbital period around the sun, leading to one being in perpetual (or near perpetual) shade. Mental approximations of the math, however, make me think that you'd likely end up with some combination of the planets being too light or the star too heavy for such planets to support terrestrial conditions. (I think you'd end up being 1/8th the mass of Earth per planet to do this with a sun-type star at 1AU and the second planet roughly as far away as our moon.) So the previously-suggested halo orbit is probably the more believable (albeit less stable) option. 

If terrestrial conditions aren't required, then you can just look up the basic orbital mechanics equations on Wikipedia. First calculate the orbital period of your desired planetary set, and then see how far from your desired stellar mass you'd have to put it to make the periods match. (You can adjust the surface gravity of the planets more-or-less independently of their mass by adjusting their density, just keep in mind that density is based on what they're made of, and a solid ball of uranium wouldn't be conducive to supporting life.)

Do keep in mind that, if the outer planet really is always completely in the shade, it's going to get really cold. Like, nitrogen snow kind of cold. Calculating how much of the outer planet would actually be shaded can be done from the relative diameters of the sun and the inner planet and their distance for the shape of the inner planet's shadow, and the distance between the two planets for what diameter that shadow will be when it gets to the other planet. You probably want at least some sunshine, or else your people will have to live around the terminator of the inner planet instead.