Networks

Hi,
I am facing a weird roadblock at work. We are planning to move our webserver from DMZ to intranet and yet make it available from internet, with SSL connection. Since encrypted traffic is not allowed inside intranet, we need to terminate the SSL traffic at a SSL accelerator in DMZ.

But our inhouse appliance is designed such that it reads x.509 certificates and then authenticates (It uses the certs for few other purposes). Can we just use certificates for authentication and not encrypting (since its not allowed). If so, will the Cisco SSL accelerator pass the certificates after decrypting the traffic?