The two Boeing (read Honeywell) types I've flown only use the initial position to help with alignment (in the non GPS days). They updated the position on the runway when you set T/O power, hence the need to add x00m to the position if you did an intersection departure.
I think you could be 10 miles out with the initial position and still not have problems as it would be corrected during alignment then updated on the departure runway threshold.