threegreatkids,
The Bible study in Preparing has two parts. One part is woven within the history study matching the Bible with its chronological place in the history study and with reading passages from the Bible that directly relate to the history study. The other part is a study of various Psalms, which is completely separate from the history study. This part is meant to be more character training and memorization in a quiet time type setting.

The Bible related history study would not fit well out of the history context. The Psalm study would be fine on its own.
In all honesty, the true preparation for CTC comes from the written narration lessons, the discussion questions, the oral narration pratice, working through the projects by following directions independently, the research skills, the vocabulary, and the science notebooking/experiments/answering questions found within Preparing Hearts. Those are the parts of Preparing Hearts which will prepare kiddos for CTC. So, if you're not choosing to use those sections of Prepraring, then you'd most likely not need Preparing Hearts.
Kiddos who place in the CTC level on the placement chart can use CTC without having done Preparing Hearts first, however it will just take a bit more training on the part of the parent to get kiddos to the level of independence planned for within CTC.
Blessings,
Carrie