Yes, for player-controlled units, Quick Strike is optional. This means that if a Quick Strike unit is grouped under another unit that is defeated by a spire, it can still attack with normal timing because the timing for Quick Strike has passed. This is assuming the unit on top of the group did not itself use Quick Strike, in which case the next unit in the group cannot attack that turn because the group can collectively only attack once per turn.
AI-controlled units with Quick Strike will always choose to use it if possible. Again, if a Quick Strike unit is revealed after the Quick Strike timing has passed, it will still attack with normal timing if it still has an attack to make.