Yes, this will get you!
The trick here is to do the GetCount inside the calculate value. A little Python goes a long way in ModelBuilder!
"Output feature class" is the model element for your shapefile that you want to delete if it is empty.
You should have Output feature class be precondition for this Calculate Value tool so it will run at the right time.
expression:
DeleteIfZeroCount(r"%Output feature class%")
code block:
def DeleteIfZeroCount(inFC):
import arcpy
if int(arcpy.GetCount_management(inFC).getOutput(0)) == 0:
arcpy.Delete_management(inFC)
return True
else:
return False