... or one can use the polygon property of the extent and use the intersect method of the polygon like this:
import arcpy
ext1 = arcpy.Extent(1, 1, 4, 4)
ext2 = arcpy.Extent(2, 2, 5, 5)
print ext1.polygon.intersect(ext2.polygon, 4).extent
which returns:
2,00000190734863 2,00000190734863 4,00000190734863 4,00000190734863 NaN NaN NaN NaN
It will return:
1,#QNAN 1,#QNAN 1,#QNAN 1,#QNAN NaN NaN NaN NaN
... when there is no intersecting polygon.