Well one of the best ways to find out if you'd be competative is to post all your statistics so we can take a look.
BUT, before I answer your questions, I think really just need to remind you that work experience is just one aspect of the application (although an important part). There is the GMAT, GPA, Undergrad School, Essays, Interview, Resume, Age, Race, Gender, Life Story, Awards, Extra Curriculars, etc...
So to answer you question in general, YES, it is possible for people with "normal" work experience to get into Top 20 schools. A lot of your application is going to be dependent on how you phrase yourself in your essays. You have to show where you've come from, why you are interesting, why you normal job experience has tought you valuable lessons, and where you want to go and how XYZ School's MBA is going to get you there. Most every applicant as an area (or two/three) that they aren't spectacularly excited about. The one thing that can help you sleep at night is that the area you are unhappy about there is very little you can do about it. In fact, many applicants are unhappy with their WE. You really have to let it go, and start working on other aspects of your application that you can improve on. For example, GMAT, extra curriculars, essays, leadership, etc... To me, it seems that you feel like you are a "normal/average/below average" applicant in gernal but you are really just basing that on your WE. Imagine if in the next year you ran a marathon, gained a leadership position at a non profit, and scored a 740 on your GMAT. Guess what, you WE has suddenly been overpowerd by your strong will, drive, motivation, and need to succeed. Schools love this drive. Don't sell yourself short, you have the power to improve and become a strong Top 20 applicant. You just have to take the chances that schools want to know you are capable of doing. Then when it comes to your application, you can really mold your work experience into the experience that has motivated you and taught you, and how you will improve the students around you at the program of your choice.
If you want to go to a Top 20, make yourself a star in all the areas you have control over TODAY, forget about your WE (of course work towards promotions and raises b/c that will help) and kill it man. You can do this.
Good luck!