No one is
certain about whether or not she would've done so, but it seems likely. As
538 put it:
At a maximum, it might have shifted the race by 3 or 4 percentage points toward Donald Trump, swinging Michigan, Pennsylvania, Wisconsin and Florida to him, perhaps along with North Carolina and Arizona. At a minimum, its impact might have been only a percentage point or so. Still, because Clinton lost Michigan, Pennsylvania and Wisconsin by less than 1 point, the letter was probably enough to change the outcome of the Electoral College.
Note that the percentages are referring to a national swing, so a 1% (national) swing doesn't necessarily mean a 1% swing in
MI, PA, or WI per se, hence why the best we can do is say "probably."