You could plausibly get cosmic radiation down to modern-day-chernobyl levels through that. The atmosphere on earth does serve to reduce radiation significantly; people who live in the himalayas get roughly 4x the cosmic radiation of those living at sea level. If you could develop a similar atmosphere around Mars, even without any magnetic shield, you could get the cosmic radiation down from seriously dangerous levels of 400+ millsieverts a year, down to a manageable 100 millisieverts. (100 mSV a year is around where we know that it starts to produce cancer).
This is not good enough for humans to be exposed to full time; but through nuclear age, we've learned a lot about how the worst effects of radiation can be largely managed through shortening exposure. If humans are spending most of their time in lead-shielded bunkers, they could live manageably on an atmospheric Mars. Space travel has deadly radiation not simply because of the intensity of the radiation, but because we're talking about weeks or months of unblocked radiation. No need for that in a colony scenario.
As well, a lot of life on earth has much better radioresistance than we do. If you could create an atmosphere, you could hypothetically design an ecosystem of plants and animals with a high radioresistance; natural selection may eventually produce species with improved radioresistance as well. It's not generally a useful survival trait on earth beyond a few extremophiles, so we don't see many animals with it. But in sites like Chernobyl, plants have evolved some radioresistance in a relatively short amount of time. It's definitely something that needs more research. You might never get large mammals, which are particularly vulnerable, but plants and simple animals including insects and shellfish have much higher levels of radioresistance.
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