What are your goals? Do you just want a pilots license or do you want to be a professional pilot? If you want a pilot's license to toot around the pattern in your Bonanza, then ATP is NOT for you and your local flight school can certainly use your business.
However,
If you want to be a professional pilot, there are two questions to ask:
1) How long do you want to wait until you begin earning a living in profession,
2) How much do you want to pay to get there?
Most likely, it will take longer and cost more to get to your goals at a local flight school (and probably most any other flight schools) than it will going through ATP.
Now, about technical ability, if you do your training in a C152/C172, you will fly at C152/C172 speed. If you do your training in a Piper Seminole, you will fly at Seminole speed. There is a distinct advantage to doing your ALL of your training in a twin, versus in a single.
For example, for me having 400 hours in a Seminole, an instrument approach in a Cessna seems to drag on forever. I would bet however, that someone with only time in a C172 feels comfortable in an instrument approach, but put them in a Seminole, and they'd likely be behind very quickly.
That could catch up to you if all of your time is spent at a local airport in a Cessna 172.
Then move up to airlines and fly an RJ that has an approach speed of twice as fast as the Seminole... you get my point.
Thats one reason why ATP's RJ program is so good. Im going through it now and WOW. What an eye opener. Lots of info, glass cockpit, fast approaches, etc. A great experience and exposure to the things that airlines all want.
So, to answer your question, yeah, I think there's a real advantage--if your goal is to be a professional pilot.
Good luck.
Jeremy