Nah, GW does the absolute bare minimum so that normal people don't get weirded out and stop giving them money. Eg they put out a statement saying "hate is not welcome in our community" but then published a short story on their community page where immigrants are all evil and a "good cop" dies because he didn't murder a child on sight. 40k hasn't meaningfully been satirical since the 90s, and has gotten even worse since 8th ed, where space marines started being treated as good guys entirely unironically. It's easy to compare conflicts in old lore to new lore and see the difference. For example:

Old Lore:

• The Badab War. A space marine chapter (which had couped the civilian government of their homeworld 200 years earlier) refuses to pay their tithes after their requests for more materiel to carry out their charge of defending a region of space centered on an open portal to hell are denied. This went more or less unnoticed for 150 years due to the Imperium's colossal bureaucracy. Finally, a contingent of ships from a variety of imperial factions related to the middle-men in the local sector government that were in charge of collecting the tithe come to see what's going on, allegedly refuse to follow instructions, and are fired upon and destroyed by the space marines for suspicion of being forces of chaos and/or pirates. The space marines convince the other two chapters who share their charge of defending the entrance of the hell portal to join them in seceding from the local sector government to form their own separate space marine-led government, which is their right as space marines and not unprecedented. A fleet-based chapter of particularly assholeish space marines that happened to be nearby by chance are brought into the situation by that sector government to aid them and end up getting into a big space battle with the rogue chapters and lose. From here, the war escalates until a half-dozen more space marine chapters and the inquisition get involved on the side of the sector government, and it ends in terrible losses for both sides, one of the rogue space marine chapters turning to chaos, and the other two being brought back into the fold but sent out on punitive crusades with the assumption that they will not survive. The imperium's structure and the fascist nature of space marines in particular leads to its own downfall.

New Lore:

• The Arks of Omen. Some demon decides he's going to assemble a macguffin to become stronk and convinces other chaos forces to help him do so. Several loyalist space marine chapters fight back. The demon succeeds and brings back the ancient homeworld of one of the chapters of space marines which had been destroyed 10,000 years ago, but now it's a spooky demon planet! All seems lost but then reinforcements show up with the primarch of the loyalists (who suddenly just showed up out of nowhere) and helps them beat back the demons. It's a pyrrhic victory and the demon will still be able to carry out his plans some time in the future (in the next campaign book). The imperium (well, just a bunch of space marines really, who cares about the other factions) is heroic and is standing against the demons that want to kill everything.

It could be pointed out that the second type of "imperium vs external threat" story is not exactly a new invention, but as far as I'm aware every single campaign since the release of 8th has had the imperium as the good guys against the big bad chaos/aliens.