Is it enough if we build the overworld from premade parts and  just generate the path?

I mean I wanna add randomization to those parts, too.

But I wonder how far I have to get until I can submit it.

I think if you added randomization to those parts then you'd be okay, it'd be kind of like Spelunky where it has basic templates but it modifies them, your tactic is great for making sure there is a way to get from the start to the exit without having walls in your path, or at least if it's done well. I am not PROCJAM though so I may be wrong.

That sounds great! Building an overworld and generating a path over it sounds like a great PCG exercise. Get as far as you can, post it here and get some feedback, and then you can come back in 2021 and work on it some more :)