It depends very much on the cat & the dog & your setup.
I have a cat who never could adjust to the dogs. She was terrified of them. Every time she came around, they got excited because they wanted to sniff her & play with her, which freaked her out. Her instinct was to run & hide, and of course when she ran, they chased her, which freaked her out more. Even after nearly 3 years, she just couldn't adapt to them.
My current cat, Spooky, stands her ground. She rarely runs from them, and if they get to be too much, she uses her claws & teeth to tell them so (every dog under her domain has been to the vet for a scratched eye once and only once each haha). She has been known to instigate wrestling matches with the dogs. But she is a much more outgoing, friendly, trusting cat than my previous cat. Both cats were exposed to the dogs as young puppies, and I make sure I'm around to supervise interactions in case they do get too rough.
Basenjis do have a high prey drive, but generally speaking, if the cat can stand its ground, and you are there to supervise & introduce them to one another slowly, it could work out.
Good luck!