Question here is.. does your radiator have side coolers built into it for trans and or oil?
Coolant in the radiator is at ~15psi, trans fluid should be higher pressure, oil I'm not 100% sure of but probably whatever the engine sees for pressure. If you don't have coolers in the rad for either, then they don't make sense to be there.
The normal head gasket will pull in oil or coolant and usually will not be able to push oil into coolant. In a head, oil is dripping (no pressure) back from supplying rockers with oil and coolant is pressurized. This is why it'* unlikely that oil got into the coolant this way.
00 Regal GS: All kinds of cool stuff.