Wishful dreamer it is! There honestly isn't any point in digging unless you are pretty sure there is something to find at that particular spot. At any normal archeological site, that means visible ruins, or traces of buildings or earthworks showing up in aerial photos, radar scans, etc. Even most large structures are only excavated in certain limited spots, not stripped completely. The mound and other identifiable features have already been investigated. A battlefield is mostly dirt and rock, several square miles of it, so that's what you'd find--no archeologist would even attempt an actual dig. And like I said, it's been lived on for thousands of years, so most of what you might find will NOT be from that battle.
Better idea would be metal detectoring, because realistically there will only be metal artifacts left to find. BUT if detectoring is even legal, believe me, thousands of people have already looked! And if it is not legal, hundreds have anyway. You'll find beer cans, cell phones, car parts, nails and screws, coins up to 100 years old, and numerous clumps of unidentifiable rust (i.e., modern junk!).
Go see the battlefield! Just don't expect to trip over a Corinthian helmet.
Matthew