diff --git a/distributed/core.py b/distributed/core.py
index 1c94352d205..40372cb8fa8 100644
--- a/distributed/core.py
+++ b/distributed/core.py
@@ -543,7 +543,8 @@ async def _close_on_failure(exc: Exception) -> None:
             except Exception as exc:
                 await _close_on_failure(exc)
                 raise RuntimeError(f"{type(self).__name__} failed to start.") from exc
-            self.status = Status.running
+            if self.status == Status.init:
+                self.status = Status.running
         return self
 
     async def __aenter__(self):
diff --git a/distributed/worker.py b/distributed/worker.py
index f443237c6c9..8fe333dfb58 100644
--- a/distributed/worker.py
+++ b/distributed/worker.py
@@ -1196,7 +1196,6 @@ async def _register_with_scheduler(self) -> None:
                 middle = (_start + _end) / 2
                 self._update_latency(_end - start)
                 self.scheduler_delay = response["time"] - middle
-                self.status = Status.running
                 break
             except OSError:
                 logger.info("Waiting to connect to: %26s", self.scheduler.address)
@@ -1207,18 +1206,20 @@ async def _register_with_scheduler(self) -> None:
             msg = response["message"] if "message" in response else repr(response)
             logger.error(f"Unable to connect to scheduler: {msg}")
             raise ValueError(f"Unexpected response from register: {response!r}")
-        else:
-            await asyncio.gather(
-                *(
-                    self.plugin_add(name=name, plugin=plugin)
-                    for name, plugin in response["worker-plugins"].items()
-                )
+
+        self.batched_stream.start(comm)
+        self.status = Status.running
+
+        await asyncio.gather(
+            *(
+                self.plugin_add(name=name, plugin=plugin)
+                for name, plugin in response["worker-plugins"].items()
             )
+        )
 
-            logger.info("        Registered to: %26s", self.scheduler.address)
-            logger.info("-" * 49)
+        logger.info("        Registered to: %26s", self.scheduler.address)
+        logger.info("-" * 49)
 
-        self.batched_stream.start(comm)
         self.periodic_callbacks["keep-alive"].start()
         self.periodic_callbacks["heartbeat"].start()
         self.loop.add_callback(self.handle_scheduler, comm)