Yes, the Reaper attribute still triggers if a Unit with Reaper deals damage to a defending Unit, even if both are destroyed simultaneously.

Explanation

• The Reaper attribute states:
  "If this Unit damages another Unit by any means, that Unit is automatically destroyed."
  (page 21)

• The rules for simultaneous effects state:
  "During a game of Sanctuary: The Keepers Era, it may happen that two effects or abilities are triggered at the same time (e.g.: two Acolytes, who both possess the attribute Last Word, destroy each other). When this happens, the current player decides the order in which the abilities are resolved."
  (page 22)

This means that if both Units are destroyed at the same time (for example, due to combat damage), both their destruction effects (such as Last Word or the destruction from Reaper) are triggered simultaneously. The current player then chooses the order in which these effects are resolved.

Therefore, Reaper will still trigger and destroy the defending Unit, even if the Reaper Unit is also destroyed in the same combat. The destruction from Reaper is not prevented by the simultaneous destruction; it is simply resolved in the order chosen by the current player.

Source:

• Reaper attribute, page 21
• Simultaneous effects, page 22

Source: Core Rulebook (pp. 15, 20, 21, 22, 25)