I did not stack them before leaving my last house, nor upon arrival. However, they were stacked in the moving truck by the movers (on a NV to TX move with a stop at a storage warehouse - so changing trucks). I moved about 1200 records and there was no damage. Some of the boxes were a bit caved in on the edges, but no record damage. YMMV.
Stacking is totally fine as long as they're full! Those small size U Haul boxes are just a lifesaver for moving LPs. Do they make a heavy duty version now?