I don't know if it has any effect. The processing time between application and being called for the exam is dependent on background checks etc. and you will still do that. At my exam, I saw that they had also called on the over 54's to show up. The asked them to step out of the line where I saw they were interviewed for a short time by a judge.
The processing time between exam and oath is normally very short, was for me 2 months so I don't know if it would get any shorter than that for you.