diff --git a/src/textual/app.py b/src/textual/app.py
index 4f3ac64a59..deb932ec1c 100644
--- a/src/textual/app.py
+++ b/src/textual/app.py
@@ -1461,15 +1461,19 @@ async def run_app(app: App) -> None:
             Args:
                 app: App to run.
             """
-            if message_hook is not None:
-                message_hook_context_var.set(message_hook)
-            app._loop = asyncio.get_running_loop()
-            app._thread_id = threading.get_ident()
-            await app._process_messages(
-                ready_callback=on_app_ready,
-                headless=headless,
-                terminal_size=size,
-            )
+
+            try:
+                if message_hook is not None:
+                    message_hook_context_var.set(message_hook)
+                app._loop = asyncio.get_running_loop()
+                app._thread_id = threading.get_ident()
+                await app._process_messages(
+                    ready_callback=on_app_ready,
+                    headless=headless,
+                    terminal_size=size,
+                )
+            finally:
+                app_ready_event.set()
 
         # Launch the app in the "background"
         active_message_pump.set(app)
@@ -2383,7 +2387,7 @@ def _handle_exception(self, error: Exception) -> None:
         self._return_code = 1
         # If we're running via pilot and this is the first exception encountered,
         # take note of it so that we can re-raise for test frameworks later.
-        if self.is_headless and self._exception is None:
+        if self._exception is None:
             self._exception = error
             self._exception_event.set()
 
diff --git a/src/textual/pilot.py b/src/textual/pilot.py
index 8226eb97ee..739a66591e 100644
--- a/src/textual/pilot.py
+++ b/src/textual/pilot.py
@@ -366,7 +366,11 @@ async def _wait_for_screen(self, timeout: float = 30.0) -> bool:
         Raises:
             WaitForScreenTimeout: If the screen and its children didn't finish processing within the timeout.
         """
-        children = [self.app, *self.app.screen.walk_children(with_self=True)]
+        try:
+            screen = self.app.screen
+        except Exception:
+            return False
+        children = [self.app, *screen.walk_children(with_self=True)]
         count = 0
         count_zero_event = asyncio.Event()
 
diff --git a/tests/test_pilot.py b/tests/test_pilot.py
index 9451237fab..52a759416f 100644
--- a/tests/test_pilot.py
+++ b/tests/test_pilot.py
@@ -6,6 +6,7 @@
 from textual.app import App, ComposeResult
 from textual.binding import Binding
 from textual.containers import Center, Middle
+from textual.css.errors import StylesheetError
 from textual.pilot import OutOfBounds
 from textual.screen import Screen
 from textual.widgets import Button, Label
@@ -395,3 +396,14 @@ async def test_pilot_resize_terminal():
         await pilot.pause()
         assert app.size == (27, 15)
         assert app.screen.size == (27, 15)
+
+
+async def test_fail_early():
+    # https://github.com/Textualize/textual/issues/3282
+    class MyApp(App):
+        CSS_PATH = "foo.tcss"
+
+    app = MyApp()
+    with pytest.raises(StylesheetError):
+        async with app.run_test() as pilot:
+            await pilot.press("enter")