Invoking abilities not needed in order to charge Net Mercur
It depends. According to the official FAQ, "a player can only trigger an action or ability if it has the potential to change the game state." But the FAQ also states: 


  The Runner can boost the strength of his icebreakers outside of an encounter with a piece of ice. 


So, assuming you have a source of stealth credits and an icebreaker that can have its strength boosted, then you can do so even if it's not being used to interact with any ice. That would trigger Net Mercur's ability. 

Edit:
For further clarification, it must be noted that Net Mercur's ability can only be triggered during a run.