Basically yes they can but it's as rough as fek. He could have chased into the corner and run them along the back. Or clipped them to the surface of the plaster.
Regards the first image. It looks like the walls are dot n dab over original plaster which makes for extreme depth. Simple rectified by either deeper back box or bringing the box he's used further forward.
A long list of snagging and Personally I would be asking him to rectify this before he gets the money. If he doesn't I would be retaining the money and telling him after you have paid the plastering team the extra cash to rectify his job you will give him the remainder.
Btw I'm not a electrician just a property developers and understand the difficulty faced when chasing back boxes and also the problem the plaster faces to rectify poor back box installation.
A electrician who has pride in his work would install the boxes correctly and a decent plasterer can rectify any problems when they are don't have pride.