The answer is sometimes.

Think of what the archaeological remains would be: armour, weapons, human remains, animal remains. There may be some destructve elements, like a burnt layer. Now look at the site in the documentation. What is the nature of it's significance?

Marathon was a huge victory for the Greeks, and they buried their dead there. So no, there is a lot of material likely underneath the ground. It's a site that is still one of significance, one which has not diminished since that era - it represents Greece's resilience and martial ability. Excavation would likely be seen as a sacrilege, not to mention to simple fact that the act of excavation would have to justified archaeologically as well - what would this excavation teach us? Will it be worth it? This applies to many battlefields - especially when it's known that the dead were buried on site.

We know that ancient battlegrounds were also tourist attractions through the ages. Surface finds and easily transported artefacts made their way off-site, both in the atermath and throughout the ages. Taking an enemy's helmet from the battle you fought in home to dedicate to your local temple was not an uncommon practice, a sybol of your victory, and more importantly, their defeat. A lot of the material would have found its way off-site before the bodies were buried. At this time, there were different values associated with death and human remains, so our attitudes to the dead, and the war dead, can be very different. Waterloo is an example - people were arranging tours to view the site within weeks, and picking up a souvenir was the desirable - anything from musket balls, livery and even soil to bits of bone. It become a must-see destination or stopping-off point for a traveller in the decades following the battle.

Don't forget, there are battle sites that have an extraordinary amount of material. They are typically battles whose location was unknown or lost - the rediscovery of Roman remains in the Teutoberger Forest is one example. There was also the battle of Mons Graupius, whose location is still a mystery. They may yield significant material.