NAT Extendable on Cisco IOS

Can you check if my explanation below is correct?
After R1 receives a ping packet from S1, R1 does routing first and then NAT.

  • Routing first: for destination 192.168.13.3, R1 will use the outgoing interface G0/3
  • Then NAT: [s=192.168.1.1, d=192.168.13.3] → [s=192.168.12.100, d=192.168.13.3]
    After ISP2 receives the traffic from R1, ISP2 won’t be able to reply as it doesn’t know how to reach 192.168.12.100

Another question is:
Is there a way to make sure that when we ping 192.168.13.3 from S1, the ping will work? If Cisco already implemented the “extendable” keyword, they should have implemented a way to make the ping work too. It doesn’t make much sense to me.