If you can work out the ventilation issue and the basement as it exists today doesn't have a moisture problem, I'd say go for it.
But then, we have been keeping a small flock of elderly bantams in our indoor bird room...right inside out house...for several years.
It does get dusty particularly during molts, so we've got a large air filter operating inside that room. There's no smell because we remove manure daily to be composted outdoors. We use a poop tray under the roost, and spot clean the shavings.
Before we moved our old gals indoors, they lived in an outdoor coop with attached run for ten years. Because I used welded wire with 1/2" by 1/2" openings everywhere, we never had a single mouse inside the coop or run. Outside the coop/run, sure. But never inside. There was no way for them to get in. So mice are not an inevitable problem.
I don't have any experience with deep litter. We always used sand in our coop outdoors and scooped droppings out of the sand. You might want to consider sand bedding rather than deep litter...keeps things drier.
Other people have raised some good questions about whether there are other hazards in the basement (such as wires, loose insulation, etc.) So you should go around your space with a critical eye.
In my experience roosts certainly do get manure spattered, but the thin plywood that forms the inner walls of our outdoor coop is fine after a decade of use. If you're concerned about this, you could always line the walls of your basement with something easily washable, like those polywood plastic panels.
