A better answer is yes, but ...
For example, there were 87,000 survivors of Hiroshima and Nagasaki. By 1992, 40,000 of them had died, but the estimate is that only 690 of those deaths were due to the radiation - that's about 1.72% if I've done the math right.
And if the doc sent you for a whole body CT scan, you'd probably be happy to have it done (though you might not be happy about the reason for having one). The dose of radiation you'd get from that is equivalent to dose you'd have got if you were 1.5 miles from the centre of the Hiroshima explosion.
So, there is a risk to radiation exposure, but it may not be as high as you think