how long would the life of a biologically immortal individual be, on average, until they get killed by something other than age?
And when? A couple of hundred years ago, they wouldn't live any longer immortal than mortal. They'd all die of disease by 35. Nobody actually dies of old age. 100% of deaths are attributable to lack of oxygen to the brain, almost always following some sort of organ failure. So it's kind of an intractable problem.
I'm not sure anyone has done the calculation in modern society. I do remember being amused by a 6th form statistics problem at school, in which sparrows were deemed "approximately immortal" and were thus killed off at a rate proportional to their numbers, rather than as a function of age. I presume this is what you are getting at, i.e. if human lifespan were determined by being killed by accidents, rather than age, how long would they last. But as Dave says, it's hard because of the multitude of diseases that are to some degree age-related: e.g. cancer, to name the most obvious.
I've seen the calculations on this. It isn't an "intractable problem" because we keep very good statistics (in the US, at least) on the cause of death for people. First, you'd have to decide if "immortal" includes immunity from all forms of disease. Assuming that's what you meant, and the only way to die was from physical trauma, the number I saw was in the neighborhood of 1000 years, on average. I have a feeling that we would be MUCH more careful about accidents if that were the only way for us to die, though...