I have not done site to site IPsec VPN where one device is using a translated private address where the platform is ASA. But I have done this successfully where the platform was IOS router. It worked just fine on the routers and I can think of no reason why it would not work on ASA.
The key thing is that there must be a static address translation for the VPN peer private address. A dynamic translation will not work. And in your example the firewall in the middle must have access policies to permit incoming traffic for ISAKMP (UDP 500 and UDP 4500) and for ESP (IP protocol 50).
HTH
Rick
HTH
Rick