Yes it is possible.
Connect:
Mega Mini
+5 VCC
Gnd Gnd
Rx Rx
Tx Tx
Connect Mega Reset to Gnd.
This puts the Mega into reset, and lets the USB/Serial chip talk to the Promini.
Select Tools:Board: 5V Promini 16 MHz
Start download - when IDE shows "compiled xxx of 32xxx bytes" press reset on the Mini.
May take a couple of tries to get the timing of the reset press correct.
Easier to see if you select File:Preferences and enable Verbose outputs.