GH-49654: [R][CI] Add check for non-API calls onto existing r-devel job (#49655)

### Rationale for this change

I wanna know when we get NOTEs about this so we don't need to wait til CRAN pings us

### What changes are included in this PR?

Add check to r-devel jobs

### Are these changes tested?

Those CI jobs should fail now

### Are there any user-facing changes?

Nah
* GitHub Issue: #49654

Lead-authored-by: Nic Crane <thisisnic@gmail.com>
Co-authored-by: Jonathan Keane <jkeane@gmail.com>
Signed-off-by: Nic Crane <thisisnic@gmail.com>

Author: thisisnic

dev/tasks/r/github.linux.cran.yml

@@ -48,13 +48,25 @@ jobs:
         env:
         {{ macros.github_set_sccache_envvars()|indent(8)}}
         # setting ARROW_SOURCE_HOME='' here ensures that we use the cpp source copied into tools/
-        run: archery docker run -e ARROW_SOURCE_HOME='' -e SKIP_VIGNETTES={{ '${{ matrix.config.skip_vignettes }}' }} r
+        run: >
+          archery docker run
+          -e ARROW_SOURCE_HOME=''
+          -e SKIP_VIGNETTES={{ '${{ matrix.config.skip_vignettes }}' }}
+          -e _R_CHECK_CRAN_INCOMING_=false
+          r
       - name: Dump install logs
         run: cat arrow/r/check/arrow.Rcheck/00install.out
         if: always()
       - name: Dump test logs
         run: cat arrow/r/check/arrow.Rcheck/tests/testthat.Rout*
         if: always()
+      - name: Check for R CMD check NOTES
+        run: |
+          if grep -q "^.* checking .* \\.\\.\\. NOTE$" arrow/r/check/arrow.Rcheck/00check.log; then
+            echo "Found R CMD check NOTE(s) in output:"
+            grep -n -A8 "^.* checking .* \\.\\.\\. NOTE$" arrow/r/check/arrow.Rcheck/00check.log
+            exit 1
+          fi
       - name: Save the test output
         if: always()
         uses: actions/upload-artifact@v4