Poodle attack only affects version 3 of the SSL protocol, and does not affect later versions. There is a lot of confusion, however - the SSL protocol was renamed in the late 90s, and what was originally supposed to become SSL 3.1 became TLS 1.0. Even though a final version of its specification appeared in 1999, it's still common to use the term SSL to refer to both SSL and TLS. Please check out our blogpost on Poodle attack for additional information and links.
This means that it should be easily possible to make ServiceStack immune to Poodle attack even without having to plug our TLS/SSL implementation into it by disabling SSL 3.0 and only allowing TLS 1.0, 1.1 and 1.2. If it uses .NET's HTTP Listener, this can either be done by editing Windows registry or using a special tool from Microsoft.
Combining our TLS/SSL implementattion with ServiceStack might be possible as well, but that would require using a different HTTP server than .NET HTTP Listener. We don't have experience with ServiceStack, but even if it does support different hosts (it might be possible to run it on OWIN, which would make it possible to use this, for example), the host would still have to be modified to support our TLS/SSL implementation. And as I wrote above, this might not be really needed.