Yes, fiberglass insulation does hold water from water pipes. Fiberglass pipe insulation runs a very low risk of holding water from pipes, but in the event of a leak, flood, or maintenance in which it gets wet, this could be a problem.
When used as intended, fiberglass pipe insulation with an encapsulated paper jacket does not support mold or mildew growth. It also resists water when exposed to intermittent, short-term precipitation — such as condensation or during construction.