Certainly worth a try...
If you do attempt it, please keep us apprised of the results (and how you cleaned it). "Before and after" pics would be great!
It would be a valuable learning experience. I have always been afraid to try any type of cleaning, but have also never had one this soiled. So in this case, there's really nothing to lose
I have always theorized that kids often spilled their Coke on these (at the games) and that's why so many have that rather sticky, dark type of staining. Not sure if that's the case here, or if that dark grime is attributed to something else...
Please be sure to let us know how this turns out!