One is qualified to hold a mechanic certificate when graduating, but that's about it. One isn't worth much as a mechanic. It takes years on the job to really learn anything about aircraft maintenance. It's one thing to be able to drive a rivet or torque a fastner. It's another thing to be able to properly exercise the privileges of a certificate.
I dealt with some graduates of a certification program with a college a few years ago who couldn't properly remove a screw. When they buggered it up, they'd never seen or used a screw extractor. One genius was going to carve up the floor on a C-130 to get at the back of the fastener.
Your question specifically regarded whether completing such a program would enhance your value as a safety specialist. It might enhance your credentials by giving you one more item on a resume, but having the certificate wouldn't make you a mechanic. It would make you the holder of a mechanic certificate, and there is a big difference.
Getting the mechanic certificate is a little like getting your private pilot certificate. It would give you a taste of what's involved, but that's it. It wouldn't really be a springboard to enable you to have a good understanding or grasp of aircraft mechanics, any more than getting a commercial pilot certificate gives you any level of expertise or understanding of what it means to fly professionally. Getting the certificate is the first step, the proverbial license to learn. That's it.