Philippe the Original is one of my favorite LA restaurants, and I might stay an hour just to look at all of the train models.
The CS (Train 11) is scheduled to arrive 9pm, the connecting train leaves 10pm and is the LAST service (Amtrak or Metrolink) to Anaheim. We call the CS the "Coast StarLATE" because it is chronically late--sometimes by hours, so I'm wondering more whether one would make the connection at all, let alone getting to Philippe's. If you don't make the connection, I'm assuming they put you immediately on a bus and the Philippe's run is off.
If you really do get in at 9pm, note which platform Amtrak 796 (Pacific Surfliner to San Diego) is departing from.
GO STRAIGHT TO THE TAXI LINEUP and if there is no line (cabs are rare in LA and sometimes there's an hour wait at LAX) because people are still waiting for baggage, take a cab to Philippe's. It's down the street, but you will need the time. At 10pm Philippe's should be slow (if a basketball or baseball game hasn't just gotten out--check schedules).
It's laid out like an old-school deli like Katz' in New York; the procedure is
1) Stand in a server line; at that hour there may be only one.
2) Look at the menu if there's time; if not, order a French Dipped Beef Sandwich with Swiss, a slice of Banana or Chocolate Cream Pie (if out, substitute another pie), and two coffees with milk in them, TO GO. Coffee is $0.09, I kid you not. If you like the exotic you could also order an extra sandwich--a Dipped Lamb--for breakfast.
They also serve wine but you can't leave with it; leave it to a deli in LA to offer red wine with that sandwich.
3) Pay the cashier (a different person behind the counter, NOT the door cashier); it's CASH only. Leave a tip on the tray as your food is being prepared.
4) Facing the counter, turn right until you see the counter with the water glasses (self service); turn left and head toward the far room. Before you pass a sort of doorway, note the Circus posters. Past the doorway, turn right and have a seat in MODEL TRAIN HEAVEN. If you love model trains, you're going to be rolling around on the floor; note it is sawdust-covered by tradition.
5) Eat something if there's time, take a picture. Since you packed to-go there's always time to eat on the train.
6) Walk swiftly back to LA Union station for your train. As with any LA street, if you have a hat or scarf or t-shirt that's red or blue, take it off or cover it up. It's not a great neighborhood and you'll run into panhandlers, but in LA there are worse.
There are few, sometimes poorly regulated cabs in Orange County, but what there are will almost always be there for that last train in Anaheim. You will observe that Anaheim Amtrak is in the Angels Stadium parking lot which literally has hundreds of free parking spaces; it's a great park-and-ride for long trips.
If you somehow miss the connecting train, call Supershuttle or Prime Time Shuttle, they can take you to your Anaheim hotel.