Almost certainly, since both passenger tires seem to be on firm ground. I love my rear locker, but being locked doesn't make your rig invincible. There will still be plenty of ways to stick your rig if you decide to go for the install, but the difference in most situations is pretty strong. Most of the trails I know would be very difficult open diffed. Some sections would probably be impossible, although a highly skilled driver might make the difference. Just remember that the increase in traction a locker will give you is proportional to the aggressiveness of your tires - both wheels turning in muck might not make a huge diff if your tires can't bite. Tires alone would probably have shifted the scales in your favor.