I would say it depends. I have had five. None spent a lot of time in a crate after puppy stage, or in the case of adults I adopted, a short period until I felt I could trust them. Some had the run of the house. Others I confined to specific rooms. None were particularly destructive although there were occasional incidents, particularly with separation anxiety. That said, I did not leave them for hours on end. Generally not longer than four hours at a stretch, and trust was a gradual thing. My most recent boy was an anomaly. After some initial hiccups he did not get into things or rip things up. He graduated to unrestricted access to every room in the house.
In summer a good dog run is a blessing. Mine was as big or bigger than the average back yard. My girls loved it out there and I could leave them for hours without repercussions other than a "construction project", a "cave" in the middle of the dog run that got progressively bigger. I let them have their fun with that. They also had an insulated house to use if the weather was inclement. In the house the girls had either the kitchen and laundry room, or the sunroom when unsupervised. They did not abuse the privilege.
I would say that you shouldn't get a Basenji if you can't give them adequate time and exercise. They are social and want their "pack" with them for company. When I had multiple dogs they were company for each other, but two or more may also find inappropriate ways to amuse themselves. Maybe you could consider an older, settled dog to adopt that has a known temperament and is either not destructive or familiar with being left crated?
and a 3 year old fake Basenji, that stay loose with no problems. We've had up to 4 at a time that stayed loose.
