Just thinking about what shipboard life would be like. A few comparisons:
A Nimitz-class aircraft carrier is a bit under 350m long, has a beam of about 40m (the flight deck is wider, of course), and carries a crew of roughly 5,700 including air wing personnel. She obviously doesn't have the life support requirements of a voidship, but she also has a crew that lives in conditions no Imperial Navy rating would ever see and is really never more than a week from a friendly port, often less.
Modern subs are harder to get solid info on, but they're certainly smaller (less than 200m long) and their crews are somewhere in the 150 range. They do have life support requirements comparable to a voidship, and many are designed for the kind of extended-duration service that warp journeys entail. They are extremely mission-specialized boats, and stealth is a major design limitation for them.
A Havoc-class heavy raider is 1600-1800m long and has a beam of 300-400m. Assuming a somewhat flattened hull and limited tapering, she probably has at least 12 times the hull volume of a Nimitz. She requires full life support and logistic redundancy for long voyages, but her crew is accustomed to living conditions that makes "spartan" an understatement. Her shipboard equipment is pure 40K era gothic tech, manpower-intensive and bulky but very sophisticated in some ways.
Given all that, a crew population of ~20,000 on a Havoc is not only reasonable but possibly conservative. Low-maintainance servitors might easily add half again that number and still leave room for thousands of embarked troops or passengers. Assuming the ship's useable living space is roughly the equivalent of 1 square km of current-day real estate, a crew of ~30,000 would make for a population density comparable to Mumbai, India, which is probably the highest on the planet these days. Crowded for most of us, but perhaps roomy to a hive worlder.
Cramming in up to another 10,000 or so is certainly within the realm of plausibility, but you aren't going to be evacuating any colony worlds or taking whole cities worth of slaves without a larger hull.