Did the Manhattan Project see radiation and fallout as a benefit of the Atomic Bomb, or was it an unintended side effect?

It was known from early on that a nuclear fission chain reaction would create a good deal of both prompt (immediate) and residual (long-term) radioactivity. This is quite clear from the basic physics of it. What was less clear, however, was how that would play out in practice. As it was, the scientists who were in charge of making decisions about the targeting of the bomb largely thought they were avoiding radiation as a serious effect. The reasons were two-fold: 1. They believed that because the radius of deadly prompt radiation is much less than the radius of the other effects like blast and heat, that anyone who was in a location to be exposed to prompt radiation would already be doomed by their exposure to the other effects. 2. They believed that the high altitude of detonation they set for the weapons, which was intended to enhance the blast effects on the ground, would avoid any serious contamination from nuclear fallout, avoiding problems of residual radioactivity.

They were largely correct on the second assumption: there was practically no fallout at Hiroshima or Nagasaki, and what little there was was pretty negligible on the whole. (To put it another way, there has not been much evidence that residual radiation played a major role in any of the exposures that people got, assuming they did not enter the city until a day after the detonation or so, when the majority of any "activated" material would have likely decayed.) This is one of the reasons that people have been able to continue to live in these cities without extensive remediation efforts (unlike, say, the areas of the Marshall Islands where nuclear testing took place, or Chernobyl, or any other place that has been heavily contaminated with fission products and local fallout).

On the first assumption, though, they were quite wrong. A significant fraction of the casualties at Hiroshima and Nagasaki are attributable to prompt radiation primarily, and even those which were attributed to other factors likely involved radiation as a compounding factor (radiation + burns = worse than either by themselves). In practice, the real world of casualties, people, exposures, city geographies, etc., are far more complicated than the physicists' simple "this range is larger than this range" estimation.

For this reason the Manhattan Project officials and scientists were caught off guard when, not long after the bombings, there were accounts coming out of Japan of radiation sickness. They initially denied them emphatically; they later sent scientists to meet with the Japanese physicians and study the victims and realized they were correct. It is a somewhat shameful aspect of the entire project history, the way in which they tried to sweep the radiation victims "under the rug," but it was in part because the people responsible for making and using the bombs feared that if they let the narrative of the bombings get out of their control, that public opinion would turn against them and the United States. They feared, as well, that an emphasis on the radiation effects would also lead people to regard the atomic bomb as not a legitimate weapon (e.g., as a form of poison gas, which would be a war crime).

So to be brief: it was not seen as a benefit at all, and was something of a known effect, but it was thought that it would not be a very defining effect of the use of the weapon. Which was only partially true.

Anyway, I have written this up somewhat here, and if you want more details, see: Sean Malloy, "'A Very Pleasant Way To Die': Radiation Effects and the Decision to Use the Atomic Bomb Against Japan,” Diplomatic History 36, no. 3 (June 2012), 515-545.