Is it OK for OSB3 boards to get wet during construction?
OSB won't be completely destroyed by water, unlike MDF or similar interior laminate materials; however, like any wood product, it will swell and shrink as it absorbs and releases water, so you should typically avoid more than casual contact with water.

If you watch homebuilders putting up a typical light-frame construction home, you'll notice that the framing lumber and OSB are typically delivered on pallets wrapped with Tyvek or similar "moisture barrier"; the wood is allowed to "breathe" and so to acclimate to ambient humidity, but the covering is impervious to liquid water like rain. You'll also notice that the roof of the house is sheathed, papered and shingled as soon as the frame is developed enough to support it, and if the crew is caught in a sudden downpour while the roof is going up, they'll drape and tie tarps over any section of the roof that hasn't at least gotten a layer of tar paper. This is all to protect the OSB; the framing lumber, while it doesn't benefit from getting rained on, is much more water-tolerant, as long as the lumber is allowed to dry out completely after a good soaking before it's closed in by walls and vapor barriers. Once the roof is up, the next priority is the outer side walls, again primarily OSB, and which nowadays also get a layer of Tyvek as soon as they're up even if the final exterior siding isn't put in place for days or weeks after.