Starting to work on a game while you are still in the middle of refining your art style can be a good idea as long as you are aware that it will cost a lot of time to do both and that that first game will likely never be more than a testing-ground. Going back and redoing it all later once you are satisfied with your art would be a ton of effort and having vastly different quality of art over the course of the game wouldn't be well received by most players. But training both game development and art in one go allows you to make rookie mistakes in both regards (and their combination) early on, so you know how to avoid them once you start with a proper project.
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Thank you for such a detailed opinion on that! I agree with you that it is not optimal to start right away and that the first project is going to be a small test game. I'm okay to redo parts of it, since making games is iterative process anyway. I plan to use 3D graphics where applicable, so it doesn't mean I have to redraw everything (at least that's how I imagine it). Of course, having 3D means there's more to learn, like rigging and animation, hence I'm okay to start soon, rather than wait until I'm good at everything (it might never happen). If I can achieve "good enough" level, I'll be super happy.