The timing chain for the Valve gear and the Drive chain for the FIP are seperate chains, although the FIP is driven directly from the Crank, and the Camshaft is drive from the same Gear as the FIP Pump.
The changes in stretch of the FIP Drive chain will have little effect on the valve timing as the change is very small, but even though this is a small change, it is enough to throw the FIP out of time by just enough to prevent hot starting. I think the amount you need to retime the FIP by to overcome is in the fractions of an inch, so this will have little effect on the valve gear timing.
When the engine is running, the No.4 Injector and the CPS work together to automatically adjust the FIP timing to maintain smooth running and efficent combustion....as the Wammer stated, during the start sequence with no CPS signal or Injector 4 Pulse, the EDC takes over the FIP timing to a set point, but this set point it is trying to achieve can't be fullfilled as the static, physical timing of the FIP is out of datum due to the stretch in the chain.....
Infact the retiming adjustment of the FIP is mentioned in RAVE I have just noticed, with adjustment figures for vehicles of under 20,000km and those over 20,000km with the new Lift Cam measurements and the required tolerances.
Once the engine is running the EDC then takes its FIP timing form the reults of the CPS and No.4 Injector...hence smooth, reasonably unaffected engine performance.