Sure, it's worth a shot... but:
HBS - slim to none; if you don't have a lot of leadership experience in college or outside of work (and likely limited leadership at work given that you're an engineer by trade), you simply don't fit what they are looking for. Plus, they like high GPAs. Too many things going against you.
Wharton - similar to HBS, although not as hardcore about leadership experience. However, chances are also pretty slim.
Columbia and Sloan - you have an outside shot. I would consider these your "dream" schools or "stretch" schools. Folks like you get in with stellar execution on the apps, but you also need luck on your side.
Stern - you should be competitive so long as you put in a stellar application.