Whew! Had a tough time finding info about this one! From the California Rare Fruit Growers Association: http://www.crfg.org/pubs/ff/pepino.html

"Harvest: Individual fruits should not be picked until they are completely mature to assure the highest flavor and sugar content. Different cultivars vary, but the ground color of many mature fruits is somewhat yellow to light orange. Ripe fruit also bruises easily and requires careful handling. Such fruit should store well for 3 to 4 weeks at around 38° F under relatively high humidity. Fruit destined for distant markets would need to be picked earlier just before full ripeness. As it turns out this happens to be a good time to pick the fruit. Studies have shown that fruit in the middle degree of ripeness has the best performance in cold storage. Over-ripe fruit suffers most from physiological problems such as internal breakdown, discoloration and dehydration. If harvested too early, insufficient ripening and development of flavor and sweetness can result. The pepino dulce is commonly chilled and eaten fresh much like a cantaloupe or other melon

The gist of it seems to be that yes, that will work, as long as it isn't too early in the maturity cycle.