Absolutely Sodapop, I'm talking about the Heathrow canned arrival, leave LAM hdg 270 degrees speed 220 kts etc etc, just a matter of flying the usual vectors and speeds. Granted, it's a bit of an extreme example due to the busy nature of Heathrow and there are certainly better places to practice, but it should not be beyond the ability of even a freshly minted F/O.
The SIDs are a little trickier because of the combination of high rates of climb and dense traffic, you certainly wouldn't want to bust a level in London TMA.
Airlines that have mandatory autopilot engagement SOPs really get up my nose, and are in my opinion one of the major contributors to the current erosion of handling skills that the industry is slowly beginning to acknowledge. These airlines effectively want to have their cake and eat it too: on the one hand they require you to always use the A/P (and reap the perceived immediate benefits of increased safety and passenger comfort), on the other hand the day automation fails they expect you to magically transition to pitch and power hand flying and save everybody's bacon.
Unless they are putting you into the sim for a session of pure stick and rudder practice at least once a month ($$$$), by the time you need the skills -that you probably had to demonstrate in the interview sim- they will have eroded. You can't have it both ways: opportunities must be provided to develop and maintain proficient handling skills, otherwise you are simply sweeping the problem under a carpet and creating basic handling problems in the long term.