Since Christian was really quick with an answer , here's some more that will get you a bit closer to your full requirement. (sort of tested and only works for file geodatabases):
arcpy.env.workspace = <specify root folder here>
#loop through all folders in the workspace
for dirpath, dirnames, filenames in arcpy.da.Walk(arcpy.env.workspace, datatype="Container"):
for dirname in dirnames:
if ".gdb" in dirname:
ws = dirname
arcpy.env.workspace = ws
fcs = arcpy.ListFeatureClasses()
if not fcs is None:
for fc in fcs:
result = arcpy.GetCount_management(fc)
countvalue = int(result.getOutput(0))
if int(countvalue) == 0:
print str(fc) + " has " + str(countvalue) + " rows features. deleting...."
arcpy.Delete_management(fc)
print "deleted"