"Will digging it deeper help with evaporation?"

I assume you mean will "digging it deeper" help retain enough water for my fish to survive dry spells?

If you increase the surface area for a given volume, then that will always increase the evaporation losses (with all other factors being held the same). If you do not increase the area of your pond while digging out the fill, then the evaporation losses will remain the same.

Does your pond pass through excess water during the rainy periods? If so, then increasing the depth of your pond will capture and retain some of this water. Therefore, your pond (and your fish) will do better during subsequent dry spells. (I think that was your intent in the question quoted at the top of this post?)