Can I use Unown's "Farewell Letter" Ability to discard it from my bench if there are no cards left in my deck to draw from?
No, you cannot. The order of operations for Farewell Letter should be to draw a card first, then discard Unown. If you are unable to draw a card, then you cannot discard the Unown.
Source: TPCi Rules Team (2019-03-28)

Relevant cards

Note: All applicable cards may not be listed below.
XY7_30