Since an EH035 has roller bearings on the rod and for the main bearings, as long as there is a LITTLE oil present in the bearings there will be little if any damage done if there is no oil in the crankcase.
No so with a plain bearing engine such as the Honda GX50. Plain bearings are fine and long lasting (and are actually more power efficient than roller bearings), but they will not tolerate a lack of oil.
My knowledge of this is third-hand, but I heard of someone who was out in the backwoods in a Jeep. His struck a rock with the oil pan and he lost the oil. He managed to drive a plug he whittled from a stick into the hole but had no oil, and he filled the crankcase with water from a stream. From what oil was left in the filter and such along with the water provided enough lubrication to get him out.