> jitter of about a few hundreds nanoseconds
The 1PPS output may have that much jitter (due to it being clocked synchronously with the module's system clock) but I believe there is usually a way to query the device for the error between the 1PPS signal and the actual idealised pulse time.
Sylvain Munaut made a project using a high resolution TDC/time of flight converter to discipline another clock against the GPS idealised pusle time. I can't find a link right now unfortunately.