If it's an NDK app, then no it won't run. The Logitech Revue (aka Google TV standalone box) has an Intel Atom processor, not an ARM, unlike most every other Android device.
1. It might run. APKs support packaging more than one machine architecture for NDK code in one apk. Currently, there is built in support, in the SDK, for both ARM variants and x86. You can get add-on support for MIPS. Possibly others, IDK.
2. If it doesn't run and you have source access, and if the native code is all in C and C++, you can compile it by adding the option to generate x86 code. It will be packaged in the resulting apk file, and should be installable on Google TV, unless it uses other APIs not available on Google TV.