Add distributed tests to run-readme-pr.yml

Need to ensure this is the right runner, @lessw2020 can you please have a look -- torchchat uses the same runners as pytorch.

Author: mikekgfb

.github/workflows/run-readme-pr.yml

@@ -306,3 +306,25 @@ jobs:
         echo "::endgroup::"
 
         TORCHCHAT_DEVICE=cpu .ci/scripts/run-docs native
+
+  test-distributed-cuda:
+    permissions:
+      id-token: write
+      contents: read
+    uses: pytorch/test-infra/.github/workflows/linux_job_v2.yml@main
+    with:
+      runner: linux.g5.4xlarge.nvidia.gpu
+      gpu-arch-type: cuda
+      gpu-arch-version: "12.4"
+      timeout: 60
+      script: |
+        echo "::group::Print machine info"
+        uname -a
+        echo "::endgroup::"
+
+        .ci/scripts/run-docs distributed
+
+        echo "::group::Completion"
+        echo "tests complete"
+        echo "*******************************************"
+        echo "::endgroup::"