There is more than one way to skin a cat, and more than one way to view the question.
Yes, dispatching is excellent preparation to understanding certain aspects of flying the airplane, every bit as much as learning to fly the airplane is excellent preparation for learning to dispatch. The two are not mutually exclusive.
That said, learning aircraft maintenance is an excellent foundation for learning aircraft systems as a pilot, and to some lesser degree, understanding as a pilot has some measure of application to becoming a mechanic or engineer.
Pilots are required to learn and to do everything that a dispatcher does; learning weather, weight and balance, planning, regulation, performance, and all the other aspects of dispatching a flight are something that is a component of the training that goes into making a pilot. The big difference is that a disaptcher specializes in those functions, while a pilot does not.
Some pilots, specifically airline pilots, all but abandon those functions and may lose a great deal of their connection to planning a flight. Dispatchers do that using charts, graphs, and computers. Pilots outside of the airlines do all those functions as a regular part of their job. If one were to make some imperfect but rough comparison, one might say that the pilot position is somewhat like being a doctor, while the dispatcher is somewhat like being a nurse. The doctor can certainly do what the nurse does, and many do just that...but the nurse may be better at it because it's all the nurse does. It's a specialty.
The relationship between pilot and dispatcher is a more true one than the relationship between a pilot and a mechanic/engineer. All pilots are trained to do what the dispatcher does. In a sense, dispatching is an ATP without the flying. Not all pilots are trained to turn wrenches (few are). What goes into dispatching is what a student pilot learns from the day he begins preparing for his first cross country flight, and is something that he or she will do throughout his or her career as a function of every flight (except airline pilots, who review the work others do...the dispatchers).
Dispatchers have a very special relationship to the flight, however, that isn't at all the same as the doctor/nurse relationship, and that is called Operational Control. In a private operation, the Pilot in Command is generally the first and last authority regarding the conduct of the flight. In a charter operation, a pilot and certain company officers share "operational control" over a flight; the authority to determine if and when the flight is launched, or refused. In an airline, this is also true, but the dispatcher is also an extremely important part of that picture.
In the airline environment (and other areas where dispatchers are used), the dispatcher is the one that sees the big picture. The dispatcher is the one that considers all the possibilities, determines the weather, the fuel load, the payload, the alternates, the overflight, and all the other aspects of the operation, and who formulates it into a comprehensive flight release and flight plan. The pilot simply reviews what has been created to see if the pilot agrees. If the pilot agrees and accepts what's been presented as reasonable, then the pilot operates the flight plan as created by the dispatcher.
Becoming a dispatcher is a good way to get to know flight planning on an intimate level. There's a disconnect between the office-creation aspect of planning a flight, and the field-execution of flying it. There's a big difference between crunching the numbers and knowing that the books say one can complete the flight with X amount of fuel at Y altitude with Z winds. It's entirely a different matter to see dwindling fuel along the way with winds different than forecast, while held down at a different altitude than planned, and to be personally affected by real-world conditions in real time. It's entirely a different matter as well to have to make the decisions using that real data to ensure a successful completion of the flight.
To answer your original question, while you could view becoming a dispatcher as "getting your foot in the door," you must remember that you're learning an entire career track and embarking on it, that is only a part of what you would do as a pilot. This doesn't give you a comprehensive learning of flying, nor does it provide you with a career springboard to become a pilot. Being a disaptcher is a full time job, not really an entry level job with the airline. One can become a dispatcher and work one's entire career as a dispatcher; it's a legitimate career track. Getting one's foot in the door is more like becoming a baggage handler; this can also be a long term job, but is more often a temporary job while someone works their way into another position, or until one finds something "better." Dispatching is not the same.
Bear in mind that as a dispatcher who wants to be a pilot, you still need not only flight training, but flying hours and experience. This is very hard to obtain on a part-time basis (such as working full time as a dispatcher and trying to hold down a flying job on the side). How this impacts you directly will depend on your location and circumstances, but you're going to need to get solid flying experience behind you before anyone will take you seriously as a pilot. Likewise, you're going to have to show some dedication to dispatching, if anyone is going to take you seriously for a dispatch position.
If you're going to fly, then it's a career track all by itself, and the best way to make it happen is to take it on full time, full strength, and be prepared for the starvation, difficulty, and trials that come with it. There are places in the world where one can jump into an airline seat with minimal experience, but obtaining one's bare bones pilot certification while dispatching full time really isn't the way to do it.
I've known a few folks along the way who did what you propose, not only through dispatching but turning wrenches and other avenues, too. In my opinion, it's more difficult and won't allow you to concentrate your energies on flying, if flying is what you want to do. Certainly learning to dispatch isn't going to hurt you; the skills are transferable to flying (just as certain piloting skills are transferable to dispatching. Again, the two aren't mutually exclusive. They are, however different career tracks.