wireless xbee Ardunio network timing of mountain bike race is this possible?

Depends on how you actually write the code. The delay can be anywhere from a few hundred nanoseconds to days.

The delay can be small enough to be considered insignificant. If the delay is on the order of microseconds or less, I doubt that the delay will be observable in the measured time with respect to the actual time. Certainly the displayed value of the measured time could have more variation (between the measured time and the displayed time) than the actual delay values.

Thank you for confirming that for me, will hopefully make the project a little simpler to program and also cheaper.

Knowing what you do about the project, do you think at an Arduino FIO would be suitable to use for the start transmitter? Am I correct in assuming that I can connect the ID-12 and a photoswitch without issue or would it be more straightforward just to use an Uno board instead?

Thanks,

-Jason