I’m asking because as a teenager I lived in motels and homeless with pill-mill turned heroin addict parents and my anecdotal experiences with the broader transient public suggest a downward spiral involving substances first.
Anecdotally, as a person in San Francisco who's been in recovery 23 years, all the people I know who were once homeless became homeless because they were abusing drugs and alcohol. Sometimes mental illness was at play, too.
There's a strong selection bias in my sample set — they're all alcoholics/addicts (thankfully in recovery, thankfully housed).
We'd need a Danish style medical records system to answer queries like that, or you can study it with VA data.
Opioid use disorder is crazy common, nearly 5% of Americans (https://www.nih.gov/news-events/rates-nonmedical-prescriptio... but also 9% of the population uses cannabis (https://www.cdc.gov/drugoverdose/deaths/index.html). It's unclear how many overdose deaths happen to homeless people every year generally, and you can conclude that since homelessness is rare, so too will be "homeless given overdose death." However, the flip side - overdose death as a fraction of all deaths given homeless - can be 17% in one study (https://drugfree.org/drug-and-alcohol-news/more-homeless-die...).
So overall, I think you're right. Opioid disorder is so much more common than homelessness generally, homelessness is not going to possibly explain opioid use disorder in the general case. Of course it can interfere with treatment. However, when so many people use cannabis, and I haven't even investigated alcohol, the right idea is that substance abuse is so prevalent in America, you'd need more serious interventions earlier on. The issue that can be acted by just medical professionals, which is the prescription of painkillers due to legitimate medical visits that lead to substance abuse, I think there is action on this but I'm not sure what it is.
As another poster, Sean, points out most homeless advocates are loath to admit to this for obvious reasons.
Uncle Bob gets hurt, can't work for a while, and gets put on Percocet, but that's to expensive and has limitations. Eventually he gets on other pills, and then a neighbor mentions he sells pills sometimes, and can get other stuff.
Few years later Bob can't take pills, can't afford them, but can snag bags of H. That's stable for a second but eventually it screws his life up more, and he's homeless.
A lot of young folks end up there cuz their home life was bad and it was easy to party / forget abuse at home, and just end up stuck.