Can Termi-Nation Unity's power be used if you don't have a Mechanical Golem in play?
Sentinels of the Multiverse follows a rule of "Do as much as you can."

Unless an effect explicitly depends on a previous effect actually occurring, then any actions that cannot be performed are simply skipped.

I ran a test case in the video game version (which sources its rules interpretations directly from the game designer Christopher Badell), and here are the results, taken from the log file.

Case 1:  Greatest Legacy uses Gung-Ho to let Unity use a power.  She has no Golems in play or in the trash.  Unity still draws a card.


  Legacy uses the power on America's Greatest Legacy.
  America's Greatest Legacy's Gung-Ho tried to increase Termi-Nation Unity's HP, but they are already at their maximum HP.
  Unity uses the power on Termi-Nation Unity.
  Unity draws Turret Bot.
  Went from Legacy's UsePower phase to DrawCard phase.   


Case 2: Unity uses her power with 1 Golem in play and none in the trash.  Unity destroys her Golem and draws a card.


  Went from Unity's PlayCard phase to UsePower phase.
  Unity uses the power on Termi-Nation Unity.
  Termi-Nation Unity's Reconfigure destroys Raptor Bot!
  GameController moved Raptor Bot to Unity's deck.
  Unity shuffles their Unity's deck.
  Unity draws Brainstorm.
  Went from Unity's UsePower phase to DrawCard phase.   


Case 3: Gung-Ho Unity uses her power with no golems in play and 1 in the trash.  Unity reanimates a Golem and draws a card.


  Went from Unity's PlayCard phase to UsePower phase.
  Unity uses the power on Termi-Nation Unity.
  Termi-Nation Unity's Reconfigure puts Swift Bot into play.
  Unity draws Flash Forge.
  Swift Bot increased the action count of DrawCard by 1.
  Went from Unity's UsePower phase to DrawCard phase. (Count: 2)  


There are conditional powers, but Unity's is not one of them

If the rest of Unity's effect was conditional upon destroying a Golem, it would be worded like Freedom Six Tempest's power Sacrifice:


  Sacrifice - Destroy 1 of your cards.  If you do, draw 3 cards.