It will work, but if you can find a good instructor and a Cessna 152,
or even Cessna 172 or Piper Cherokee, I suspect you can do it for less.
Most pilots take more than 50 hours though. For private with aircraft
renting for 90 and instructor at 30 that is 120 x 50 = 6000 plus books,
checkride fee, medical and FAA test fee figure 7000. Now figure in both
cases you need an additonal 20 hours for a total of 70. You don't need
ground school, just study on your own and take a the FAA prep test
until you get 90 or better. Your instructor can answer any questions.
One nice thing about the arrangement you quoted, they usually have
their own DE and know what to expect and the failure rate on the
checkride is lower. If you are headed for pro pilot you do not want any
checkride failures, very important and worth a lot of money. I
recommend Sheble Aviation. They do a good job and don't mess around.
They get you there. www.shebleaviaton.com says their course with 45
hours of flight time is just under $5000. I am not affiliated with
them, but have got my Seaplane rating there.