You could, but there is no particular advantage (e.g time savings etc.) since the beans are already cooked. That said, you could follow the recipe for sauteéing the requisite ingredients, adding less broth. You could conceivably continue to simmer the soup in the Instant Pot or cover and pressure cook (but the risk is mushy beans, and you would certainly have to cut the cooking time significantly--I'm guessing 5 minutes or less if pressure cooked) You could as easily cook this on the stovetop and then you'd be able to monitor the progress and the ratio of broth to beans to achieve the texture you'd like. I honestly don't see the advantage to using an IP for this purpose since the great advantage of a pressure cooker is the speed with which it cooks dried beans. You'd still have to wait for the pot to come to pressure at the start, and to release pressure at the conclusion.
This recipe could serve as a template for how long to pressure-cook a bean soup using canned beans: https://thekitchengirl.com/instant-pot-vegan-tuscan-white-bean-kale-soup/; I'd follow the black bean recipe for the sauté portion and adjust using the tuscan kale recipe for the pressure-cook timing.
I haven't tried this with canned beans, but I suspect it'd still be great—just be sure to reduce the cooking time. If I were trying it, I might start with pressure cooking for 10 or 15 minutes, and see if that does the trick (since the beans will already be semi-soft, you'll want to find the sweet spot of giving the flavors of the broth-y part enough time to build, without obliterating the beans!). That said, even if your beans get too soft, I think you could immersion blend them until smooth and still have a delicious soup. Let me know how it goes if you give this a try :)
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I haven't tried this with canned beans, but I suspect it'd still be great—just be sure to reduce the cooking time. If I were trying it, I might start with pressure cooking for 10 or 15 minutes, and see if that does the trick (since the beans will already be semi-soft, you'll want to find the sweet spot of giving the flavors of the broth-y part enough time to build, without obliterating the beans!). That said, even if your beans get too soft, I think you could immersion blend them until smooth and still have a delicious soup. Let me know how it goes if you give this a try :)