My friends and I had an argument over this the other night. The rules say that the Balrog can be used at "any point during your turn." So I attempted to use him to ruin my friends day (taking out one of his places of power) and then go into decline. He claimed that I could not do this as I had started conquest by moving the Balrog and therefore could not decline. I countered with the "Any point during my turn." would imply I could do it pre-conquest as that is still during my turn. I searched elsewhere on the internet but only found discussion boards and forums with similar arguments to the one my friend and I had.
There's actually an official ruling on this very point by Days of Wonder in the SWU FAQ:
Some people may not like this ruling very much, but I don't think its existence can be denied!