xe: I wouldn't worry
too much about pigeon-holing yourself, certainly not with a mat sci degree. Once you get your M.S./Ph.D...assuming you see that as your terminal degree, you might find you have a versatile set of abilities. The most important, by any stretch, is the ability to troubleshoot and problem-solve. Ive jumped around a bunch in my short career, and I'll tell you this: working with ex-Army/Service guys is always a pleasure. They typically have a can-do attitude, and are good with their hands. The most important thing that degree will do, in my opinion, is open some doors for you. Credentials, etc. I'd say if you're feeling that's what you want to do, go for it. I could draw some umbrage at the suggestion that Chem-E limits you...but that would only be for fun
If you're doing engineering, the math will always be a pre-req, as will looking for the application side to technology. Sure, the lines get crossed in research organizations, but ultimately an engineer cares about what you can do with the science...a chemist only cares about the science...and the lines get blurred depending on personality. Best of luck - if you need anything, pop a PM.
And stay safe