Trees are normally considered extremely risky to allow to grow on a dam because their roots can puncture leaks into it. However, is it possible that a dam could be thick enough for this to not be a major concern? If so, how thick would that have to be?

I wouldn't take the chance, but since a trees root system can be as large as their crown, it'd have to be a BIG dam.

In real world dam construction, no.

Cedars would probably be ok given their shallow root structure - but I’d build the dam a little higher to accommodate the roots just in case. I would not consider any other tree on a dam that I’m familiar with other than cedars.

Trees will cause leaks. I had all the trees, including several trees up to probably 16 inches diameter taken off my first pond's dam in August 2015 when it was renovated. The guy must have failed to get all the roots out, because it leaked prior to renovation, and has leaked ever since.

Cedars might be OK, if the dam is tall enough to support the shallow root system above the water line, but cedars are messy, shedding branches and needles. Plus, they make fishing difficult.