Hi, Larry,
I agree that is a good idea if you can find a place like that. The problem is that there are a lot more folks who like to tinker with guns than there are positions in gun shops. A certificate from a gunsmith school should put you well ahead of the guys who took apart one gun and want to be gunsmiths, but there is no guarantee.
If it were me, I would seriously consider going into my own business and start accumulating capital. Start-up costs are high, plus it takes a while to get established and you have to live until you do. Also, you would want to decide what you want to work on and what you won't touch. You can specialize (AR-15 and 1911 are good areas, but rather crowded), or do general gun work. Part of the trick is knowing when to turn work away and how to do it without offending anyone. For example, fixing a cheap, century-old Iver Johnson can take a day or more, and there is no way anyone is going to pay you for that amount of labor on that gun, no matter what they say before you present the bill.
Even jobs that used to be "bread and butter", like drilling and tapping for a scope, are uncommon today with almost all factory rifles already drilled. Rechambering and re-barreling are good work, but also time consuming when done right, and there is no other way unless you want to get a rep as a poor gunsmith or even sued.
One thing you might do is to just look at this forum and all the stuff folks want done. Do you want to tackle those jobs? Can you do the work at a reasonable price and still make good money? If the answer is yes, have at it.
Jim