The problem isn't the „marriage” but the „Heterodyne” part of the plan. The combination of the two parts didn't end too well for the last guy wearing the crown. Trying it again is just tempting fate.
I would give them points for the „fake” part, but... a Mongfish? Really? Even if we ignore Lucrezia they aren't what I would call trustworthy. Adding them to a family that already tries to wipe itself out seems „not very smart”.