I don't know about using Joy, but I've run Dawn dish detergent in plain water for a short time, to clean out oil residue in the water jacket after repairing a blown head gasket. I like Dawn because it rinse out very cleanly, even with cold water.
Dutch
2001 GBM Landau 34' Class A
F53 chassis, Triton V10, TST TPMS
Bigfoot Automatic Leveling System
2011 Toyota RAV4 4WD/Remco pump
ReadyBrute Elite tow bar/Blue Ox baseplate