Hi Gbps,
Question: Is there a way through iRule to translate Client IP address to a single IP from the snat-pool for all connections during the same session?
The simple answer is yes, by specifying the SNAT Address like you are doing above but there are limitations.
If you use SNAT Automap the BIG-IP will use one of its Self IP Addresses as the SNAT Address, but each Self IP Address can only snat 65,536 connections before the next Self IP Address is used (any SNAT Address you specify will have the same limitation). Note that these are per connection and most browsers open up anywhere from 3 to 6 connections at a time to download a site faster. So depending upon the usage of the site you may need to have multiple SNAT IP Addresses (use a SNAT Pool).
Do you know if the application is capable of using an X-Forwarded-For HTTP Header? This would deliver the True Client IP Address to the application and might help your situation as well.
X Forwarded For Single Header Insert
Using "X-Forwarded-For" in Apache or PHP
X-Forwarded-For
Hope this helps.