No you will need a new 4.6L radiator. The 3.8L does not have the same expansion tank, thus unless you plan on buying a V6 expansion tank too don't buy it. The V6 has the radiator cap actually on the radiator, whereas the 4.6 as you know has the cap on the expansion tank. Now, the hoses may line up, but why risk it. A replacement one from advanced auto is $150.
2002 True Blue V6 to GT Vert
16.1@86 as an auto 3.8
2.15 60', 9.3@77, 14.4@96 as a 5spd SOHC 4.6