It would probably be more like Traveller: New Era meets ACKS than Deathwatch or Dark Heresy.
I have a love/hate relationship with a lot of the 40k universe. On the one hand, I quite like the "everyone dies" aesthetic, the laughter of uncaring gods, Space Hulk, the Ravenor trilogy, the tyranids, Mechanicus, Inquisition, and the doom of the eldar. On the other hand, there are the space marines, the tau, the ecclesiarchy, the rogue traders (who always felt a little too free for such an unfree world), and those goddamn orks. Further, for an empire where much technology is lost and forgotten, there always seems to be an abundance of powered armor, plasma weapons, and other fancy gizmos fit for cracking tanks or continents. These combined always made the prospect of running an RPG in the 40k universe somewhat offputting.
Well, says I to myself late last night, we can fix that.
Consider, for a moment, what happens to the 40k universe if, one day, the Astronomican goes out, permanently. Imperial ships in the warp at the time are lost, and further long-range interstellar travel becomes an impossibility. Military campaigns on ten thousand worlds grind to a halt for lack of resupply, and the units abandoned there must either go guerrilla, make peace, or be slaughtered. Many hive worlds, reliant on imported foodstuffs for their sustenance, suffer starvation, unrest, and descent into anarchy. The enemies of man, still capable of interstellar travel by their usual means, go on the offensive, bypassing strongpoints where Imperial units remain active, and conquering ripe, undefended worlds with little effort.
The space marines, scattered across the galaxy in forces as small as platoons, must reintegrate into human society, becoming leaders of men. Bolter ammunition, already scarce, becomes vanishingly rare, and powered armor, lacking spare parts and untended by the ministrations of the techmarines, falls into disrepair. The homeworlds of the various chapters, such as Fenris, Nocturne, and Macragge, continue recruiting, impanting, and training more marines of their chapters, but most worlds with space marine deployments lack the specialized medical infrastructure for the growth of implants from the gene-seed. On those worlds, the marines tend to form long-lived military juntas, which provide a gateway into stable, moral governments backed by tempered force.
On many worlds, the Ecclesiarchy remains in power for some time, holding forth with the doctrine that the faith of the people is being tested. They are supported by the astropath network, providing news and maintaining mankind as a single culture. As years pass, however, the astropaths begin to die off (and new ones cannot be taken to Earth to be soulbound), and salvation seems less and less imminent; many planets rebel and overthrow their religious rulers. Most of these insurrections fall to chaotic influence, but some, perhaps, are successful, staving off corruption under the watchful eyes of former inquisitorial agents with little love for the zeal of the Ecclesiarchs.
The Forge Worlds, too, weather the transition relatively well, with the beliefs of the Cult Mechanicus unshaken and its power largely intact. Many, however, suffer from resource exhaustion, turning to desolate anarchic wastelands a la the Road Warrior, and without safeguards against chaos, more still fall to the lure of dark sciences. The forge worlds are likewise juicy targets for the enemies of mankind, for while they maintain their Skitarii fighting forces, they are rich in technological plunder. Some, however, endure, arming themselves and stewarding their resources while their best minds seek a safer means of FTL travel.
And so it is that, a few generations after the collapse of the Empire, on one of these stable worlds, PCs appear. Foolish young souls with a penchant for adventure, an eye for profit, the cojones to explore a drifting space hulk, and a dream of distant stars...