lord of the rings - Would Gandalf have been promoted to the white if he had not fought the Balrog?

Gandalf was promoted to a White wizard after his body was destroyed in the battle with the Balrog.

This was done mainly to replace Saruman as he had joined Sauron (or at least swayed significantly from his path as protector of Middle Earth) so it had already become a necessity to find a replacement by this time.

It is shown (in the movie at least, I am not sure about the book) that it was chance that they even met the Balrog, who just happened to be there, and it might even have been possible for them to out run it.

So if they had been able to outrun it, or had not stuck around long enough to meet him there in the first place, so that Gandalf did not have to get his body destroyed by fighting him, would he still have been promoted to the Head of the White Council?