This question seems to imply engineers are not designers. Some are, see in mechanical engineering there are no Architects but instead mechanical engineers handle that themselves.
Thus the lead mechanical engineer who draws up the instructions for the general concept is a designer. And in fact it says on my diploma that I am a machine designer. It is just that what machine designers produce 3D objects that are milled, cast, bent, welded structures etc. And that is essentially no different form doing a graphic designers work*. Instead of illustrator i use a 3D CAD geared towards my specific needs.
Sure there are a lot of engineering niches that are not design per see, analyst, measurement and tuning. But even graphic designers are slowly being forced to this direction and industrial designers are almost exactly like mechanical engineers, with just a different focus.
SO in the end its more about what job you can land than what paper you have. There are a lot of jobs that fall in between the cracks. Like say a technical illustrator, which requires some illustration skill, but that can easily be offset by having a skill in the cad side of things.
* I work with graphic designers and sound, new media and animation artists so i know what it is they do. I do essentially the same things except i am not allowed to do so many failures and experiments due to the costs involved.