No, "bomblets" or released grenades have their own properties, though they will inherent the elemental type on their item card, and they behave in a specific way depending on the base type of grenade (MIRV/Transfusion).
Homing MIRV grenades still release plain bomblets that rise and fall in an arc, just like lobbed/longbow MIRVS. Similarly Transfusion grenades always release homing projectiles even if they aren't homing Transfusion grenades. There are however some legendary/unique grenades which have special properties applied to their bomblets that normal grenades do not, such as the Fuster Cluck, which drops bomblets as it's moving in the air rather than after detonation.