Yep. Applesauce can be used as a replacement for oil in cakes and some quick breads. I've done it on the rare occasion I've been short of cooking oil for a cake. Don't think I've ever swapped it in for all the oil though. It does give a bit different texture and flavor, I find it kind of pleasant myself. And youy will need to probably bake the cake for a bit longer too. YMMV based on your oven.

I personally would not use applesauce to fry in though. But perhaps Flying Squid's mother should experiment for use and they can report back to us on the results.