Hi Giulio,
Short answer is no; neither the CSM nor SSLM/CSM-S will NAT the original client IP address unless configured to do so...
NAT client is configured at serverfam level on CSM, SSL-Proxy on SSLM version 2.X and Context level on SSLM version 3.X.
If you're running on routed/bridge mode on your CSM you have nothing to worry about as this designs do not require NAT to be in place when configured correctly.
HTH
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Pablo