My roof is off and the metal will not arrive for a few days during which time we may get some showers. The underlayment is fiberglass. I assume it will be ok exposed for a few days.
I do not know of any fiberglass underlayments, it is generally used as a base sheet for Built-up roofing or torch systems. As a rule it is not waterproof, or use for waterproofing on it’s own, it is not like 30lb, or 40lb. organic felts that are used for this purpose.
If fastened correctly it will last for well over a week.