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.
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.