Can adding both Asc and Desc indexes improve performance?
The leaf pages of the index form a doubly linked list with pointers to the next and previous pages. This means indexes can be scanned both forward and backwards.

There is a slight difference in that currently only scans in the forward direction can be parallelised but it is extremely unlikely to justify the cost of maintaining both just for that edge case.


  could it allow SQL to search any faster by utilizing both indexes at
  the same time?


No SQL Server won't split a single index access into a multiple index access in some sort of attempt to parallelise the work.