As mentioned above, your radiator has a transmission cooler built into it. Because of this, you should be taking the low coolant/overflowing ATF situation VERY SERIOUSLY. If the transmission cooler has failed and allowed coolant into the transmission, you will very quickly ruin it! ATF won't be running out the dipstick tube unless something else has entered the system to displace it or the transmission was grossly overfilled to begin with (and even then it should bleed out the vent before it comes out the tube).

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Current stable:
1995 E320 149K (Nancy)
1983 500SL 120K (SLoL)

Black Sheep:
1985 524TD 167K (TotalDumpster™)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)