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: 
This sort of configuration may be possible if the smaller planet is located at the L1 or L2 [Lagrange point](https://en.wikipedia.org/wiki/Lagrangian_point) of the larger. I doubt this would work out in real life (and haven't done the math to determine how close or far apart they'd need to be if it did), but, fortunately, Warhammer 40k is not a scientifically rigorous setting, so you can probably get away with simply invoking Lagrange points along with a bit of handwavium to stabilize that configuration.

Also, technically, the planets would be tide-locked to their shared sun, not to each other, but the practical effect would be the same as what you're looking for.
There is a non-orbital solution as well. We've not got the technology to build it but 40k is considerably more advanced in many ways.

Have the larger planet orbiting at it's natural orbit.

Have the smaller planet orbiting in the shadow of the larger one further away from the larger planet.

As already discussed there is a problem with this, they will drift apart.

Embed a tether made of unobtanium through the cores of both planets and through space between them. That tether is strong enough to stop them from drifting apart. They now orbit as a joint unit. You would need to arrange the dynamics so that they hold the same position relative to each other (good thing you wanted tidally locked) and keep a modest tension on the tether.