It is possible that it will be processed earlier, but you shouldn't count on it. If you have a social security number, be sure to include that on the application, that will help.
Keep a copy of your application, and receipt showing the date you mailed it to the FBI. Of course using a courier will cut down on mail times.
In case you do not get the result in time, submit your application anyway - do not miss the 120-day deadline. Include a letter stating that you have applied for the FBI cert (attach the evidence) and will forward the result as soon as you receive it.
And hope for the best. They don't have to be nice about it when people don't read and follow directions

But the newest instructions seem to reflect more realism about the difficulties in obtaining PCCs...