Adam,
Yep, looks like nailed on bottom to me although it appears to be a different wood than drawer sides, possible repair? Dont get me wrong about nailed on bottoms, it did happen and not only in Philly or by London trained cabinetmakers. I have this Chippendale painted yellow pine blanket chest that was found in the Shenandoah valley with wedged dovetails (dont get me started on this) that has drawers with bottoms nailed on with very large T headed nails. Its just that the groove/bevel drawer bottoms are much more common than nailed on bottoms, why that is i have no clue. Perhaps nails were an issue? ( I would note there are those that disagree with this theory and that iron was not that big a deal in the colonies)
In any event, this blanket chest was built by a German trained immigrant in the last quarter of the 18th century and he did wedged dovetails (prettiest dovetails i ever saw, bar none) and nailed on drawer bottoms somewhere in the back country of Virginia.