I reckon it would depend on how it was failing. T4 measures the LP fuel pressure from the sensor on the fuel filter, so if the ITP wasn't pumping as it should then that would show up.
If however the pump failed like the earlier designs do due to the commutator segments wearing out then no - it will work fine up until the time it doesn't start.
Probably a bit more to it than that though - I'm sure a T4 expert can give you a more in depth answer. Sadly I don't own a T4, just a Sykes Pickavant ACR4. Good enough for what I need it to do, but a T4 it ain't.
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