I think if I was confronted with a big pile of marking on Monday, I'd expect to see a lot of it done and if it hadn't even been started I'd be asking questions about exactly why in the two weeks available it had been left till the last minute. There's being stressed, then there's taking the piss.
I had a crap NQT as a colleague and I helped them out by observing a lesson, giving suggestions, easy to implement ones like 'get then to tuck their chairs under the desk at the end of the lesson so the room isn't a tip for the next class coming in' and it was really frustrating to see advice not acted on. Made me wish I hadn't spent my time bothering to help!
It was after Christmas that concerns escalated and comments started to be made about not passing NQT year if no improvement. They were gone by Easter, told that if they didn't leave voluntarily, with the ability to complete their year in another school, they would fail and never be allowed to teach again.
Is your NQT permanent or on a year contract? Basically, if you don't think they should be in teaching, you need to be making moves now to either encourage them to look for another job (teaching in a different school or otherwise), or collecting evidence to fail them.
If you let them bimble along getting inadequate observations and being super stressed about planning and marking on the easiest timetable in the world, then you may end up with a permanent crap colleague next year on a full timetable taking up your time and energy. Competency wouldn't be any fun to organise.
You've been gentle and they still can't hack it. Don't rescue them, it's time to get tough.