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.
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.