You're right. A good pilot never stops learning, or studying.
There are a number of jobs which will permit you to turn wrenches as well as fly. Most of these jobs, however, are dirty jobs; that is; the're working jobs. Few, if any, white shirt jobs will involve piloting and wrenching.
Don't be surprised to quickly learn that having the mechanic ticket serves to keep you from flying; once an employer learns that you can fix what you break, you'll probably find yourself on the bottom of the list for flying duties. Or you'll find yourself flying to less than idea locals to fix what other people break.
Having a mechanic certificate has it's advantages. It does give you an edge in some jobs (FE jobs, in particular, but working jobs, as opposed to straight "driving" jobs).
I got my first corporate job (and not coincidentally, my first jet job) because the corporate department needed a director of maintenance/copilot. Soon I was flying 15 hours a month, and turning wrenches about 80 hours a week.
One problem I've found in the past has been confusion on the part of a potential employer. A quick glance over my resume will show that I've turned wrenches for many former employers, as well as flying. The first question I sometimes get is, "are you applying for a mechanic position, or a pilot position?" Recently a friend at a local college offered me a job as...director of maintenance for their flight department. When I suggested I would be interested in doing some part time instructing there, rather than turning wrenches, they expressed surprise.
Conversely, several days ago I was offered a position with an ag operation. It involved flying ag, flying fire, showing and selling airplanes at airshows, managing the airport, and working/managing the shop. A big selling point to getting the job (aside from previous ag, fire, sales, and management experience) was the A&P. Having an inspection authorization will make a big difference, too. In this case, it was an offer to move into ownership, as the current operator wants out. Again, a working job, as opposed to a button-down job, but it all depends what you're looking for. In some cases, the A&P will be helpful, others detrimental, and others, it won't matter. For some jobs such as this one, it's essential.
It all depends on your career aspirations. Having the A&P is a good place to fall back; it's a good way to secure jobs in the event that other jobs are no longer available. However, if you're looking for the fast track to the airlines, you'll probably find that being a mechanic may slow you down a bit. This is especially the case if you take jobs that require an A&P, or which will use your mechanic's services in addition to your flying. A strange paradox, but true.
What are your goals?
