No need to wait for the hard copy of RTR(P).
You can submit your application for conversion of foreign license to DGCA, along with the receipt of submission from WPC (challan).
You will have to mention that on the application to DGCA. DGCA will send you a letter of shortcoming regarding pending RTR(P). Your conversion will be processed after you submit the RTR(P) hard copy from WPC. This does not affect the date of submission for conversion.
There is a circular about this. http://www.dgca.nic.in/circular/FCL3_2010.pdf