Well, I'm not sure if I should open a can of worms or just answer the question as stated.
Couple of things to note.
Tommy is right on about qualifications to get in the door in the aerospace world.... Most want at least 5 years verified experience... A Looooong personal background check if you work for a carrier. And a high level of competency in GTAW of thin material.
If you have military experience (2219 or 1595 certs) bring the paper to the interview and of course note them on your resume'.
Certs themselves are good to get an interview but will NOT cross over between contractors, you will be tested again. I would not advise getting certified at your own expence unless a specific employer personally recommends it to you, on the other hand I would be skeptical of any employer making this request.
I carried my 1595 cert cards for many years after leaving the military. They did open a few doors, but nobody has ever hired me without a welding test.
As far as FAA goes...... The FAA requires no welding certs. They act more like ISO when it comes to welding, in that they will check to see a company is in compliance with whatever contracts are imposed on the job. In truth, any swingin son of a gun with an A&P (airframe & powerplant) now a days also known as AMT (aircraft mantianence technitian) liscence can weld on an aircraft or sign off on a welded repair that somebody else did under their supervision. Your garden variety A&P has about 3 weeks oxy-fuel training during a 4 semester training course, most aircraft mechanics are not called upon to weld, so it is a very minor part of the overall training curriculum... it is bloody terrible. If there are any AMT's out there who know of traning institutes who actually provide GTAW training to a certifiable standard as part of their AMT/Associates program, do chime in as I would like to be able to recommed their school.