Moving from mechanic to engineer is nearly impossible. Moving from Mechanic to supervisor is almost as hard.

Think of it this way. It will take you at a complete minimum 4.5 years to become a mechanic. This is if you get hired and start classes after the 6 month probationary classes (Ignoring Temporary Mechanic status). This is the starting point.

Now, to become a supervisor you have to become respected in the office, one of "their" guys. how you go about this can alienate you. They will approach you, but most likely they'll hire from some other company to fill that role.

To become an engineer: 0.0000000000000000000001% chance. It's "there" but not really (At least not from the field). You could apply at a company to be an engineer after working in the field, but they are not Union, and are not compensated as well. So kiss your benefits and pension goodbye (This occurs with being a supervisor, too. And you have to turn in your union card).

I know of a guy who is essentially an elevator Guru, can do just about everything in the trade and has an engineering background he got a job as a field engineer with another company, but I think that he was taken for a ride and will never be an engineer, but was stolen away to hurt business.