Hi,
To my understanding you wont be able to ping an ASA interface from behind another interface.
For example host on "inside" pinging the "outside" interface IP address and vice versa.
There is alteast one exception to my understanding.
When you have a VPN connection configured on the "outside" interface and want to ping or use management connections to "inside" interface you can use the following command
management-access inside
Which will enable the connection/ping coming from the VPN connection through "outside" interface to reach the "inside" interface.
- Jouni