Three months of outdoor exposure suggest that laser test paper can survive use as a plant tag for one growing season, at least when it remains flat:

The two upper tags demonstrated the paper has no flexibility worth mentioning, so it cannot become a tag wrapped around a stem.
The two lower labels spent their time tucked into a window frame where they got plenty of sun & rain without the benefit of a backing plate. Looks good to me!
Contrary to my expectation, the craft adhesive sheet behind this label survived intact, although the label itself took some damage, perhaps from the more direct sunlight out on the deck:

In any event, they look Good Enough™ for our simple needs and next year’s plants will be properly labeled.