Aadhar isn't mandatory but it speeds up the process. I got my passport renewed last month. I filled online application in march, got date of April. Went to the passport office with all required documents etc. Took 2 hours in the office.
1 week post my visit, police inspector called me to setup the date and time as to when he can visit my place. He came on the fixed time. Took signatures of two references and left. Passport came the next week of his visit.
So in all from the day of my visit to the office, it took 2 weeks to receive the passport. Hope this helps.