I imagine it will recover if you continue to care for it especially as you don't intend to grow it to produce fruit. Mangos are typically grafted in order to get the desired flavor. You can also get dwarf varieties which would probably do better in the long run for limited growing area as mango trees typically get taller than a typical room.

Hi there, think your plant will recover. What size is the plant? The smaller the plant the more damage snapping the end off the taproot would do I would think as small seedlings dont have the larger more established root system to counteract any loss. Has it started to droop? If it hasn't then I'm sure all will be ok as I guess it has other roots to compensate for the bit you snapped off. In any case, continue to look after it as normal and fingers crossed all SHOULD be ok.
Here's a pic of my Kent mango I planted in spring 2007. It grows in alternate stages of stem growth and then produces a whorl of leaves whch are thin and bronze pink hardening to a tough deep glossy green colour. Watch out for spider mites which like a dry atmosphere, I mist mine regularly with tepid water.
Gill.