@Tych I suppose so, but for that it would also require an actual body to use the magic from (since it requires mana(that's what it was called in this series, right?)).
However, the act of mind/soul corrosion that they are doing is described in the novel as a simile heresy attack from outside the System. In short, if the target had Herersy immunity, this mind/soul take-over wouldn't work, and if the resistance is high(such as in Mother's case), then it takes a long time.
So technically speaking, this mind/soul corrosion is already an Heresy attack, just one that isn't an Heresy spell and that doesn't required mana to use.
Also, while the split-minds have kept their nicknames, they no longer have those functions since they aren't in the main body anymore. However, once they do take-over Mother, they'll be able to use Mother's body.