Yes, very large mango trees, with deep tap roots, can withstand a lot of drought and even hold some fruit; however, their production would be optimized by keeping the topsoil reasonably moist--- far fewer tiny fruits would be dropped.
Remember that most fibrous feeder roots and their hair roots are in the top foot or two of the soil. Hair roots acquire most of the minerals absorbed by the tree. As hair roots die off in drought, mineral concentrations going up the xylem drop, and small fruits drop off in mass--- all the more so if the minerals most affected are Calcium, Boron, and Zinc.
If overhead or sprinkler irrigation is used, you may want to run it after sun-up, to avoid adding to anthracnose.