Not really. It takes time for the signal behind to clear, so I’d guess that eastbound trains would be overtaken at Thorpe Park/before Garforth, westbound at Cross Gates, if there was four-tracking between those two stations only.
(Which is more or less what
@YorkshireBear wrote above.j
Adding a further station at Osmondthorpe/Killingbeck would slow the stopper into the clutches of the next fast service, and you’d be back to where you were.
All of those suburban stations ideas were abandoned (apart from East Garforth) after the first few WY Railplans, probably as traffic levels increased.