What is the current limit on each phase of a 160 kVA three-phase UPS?
Yes, a 3 phase 160kVA supply would mean 3 single phases each at 53.3kVA.  

The factor of  \$\sqrt{3}\$ arises in the power calculations when using a line-line voltage.

Note that the UPS may or may not be able to support unbalanced loads.