I did pretty much all of my PPL training in my Mooney. Took me about a year in my own plane with a lot of down time fixing & upgrading just to get my PPL. You are limited to the instructor’s time too so any airplane issues that come up, you are stuck. It took me longer than had I just rented or went through a flight school, cost more than a flight school.
You may be limited to which plane you buy. I had to find a plane with co-pilot brakes which at the time there was only one, the one I bought. I had to do a lot of upgrades & updates to get it where I wanted it. Going on 3 years now with my Mooney and I’m about to hit 250 hours in it but I lack the experience of flying several different airplanes which you would likely get going through a flight school. It’s doable for sure & now that I’m done I don’t regret it but just plan on everything taking longer than you think & it will be more challenging as an owner. DM me if you want more info.