With that logic, a 25 capper reducing his index to 20 over 5 years should be able to play the Tour some day. It may take him 85 years to get his game in shape, but your presumption is that improvement has no limit. That may not be the case.
I'd say with enough money (to take time away from work, pay bills, afford lessons, range time, playing, fitness, equipment, etc.) yeah someone with decent athletic ability could get to scratch in a year. Could they get to the tour? Not sure. Depends on the person. Maybe scratch is as good as they can get. Maybe they can get to a +2. +2 isn't going to win any money out there either though :)