Spikes and Prototypes are Okay; Retconning Project Plans Is Not
I was planning to go onto the implementation phase and then to reverse engineer my work.
From a project management point of view, this is not okay. Planning is hard, but not planning creates technical debt and problems for the project and the organization down the road.
Waterfall is about upfront planning. Agile is about just-in-time planning. Neither methodology allows for "ready, fire, aim" planning, which is what you're describing.
From an engineering point of view, it is certainly allowable to do a project spike or create a prototype with minimal planning in order to validate an idea or create lessons-learned for creating a more permanent implementation. However, what you're describing here is more like retconning your planning documents to fit whatever you end up with, which is not a good project management or engineering practice.