Yes, the type of phone you have does not affect whether you can be on the approved call list. Prepaid cell phones, postpaid cell phones, landlines, and VoIP numbers are all eligible. The carrier and payment method behind the number are irrelevant to the facility's approval process. What matters is the number itself and who it belongs to.
The inmate generally controls who goes on their call list, and the facility's review focuses on the person requesting to be added rather than the technology they are using. A prepaid number is processed the same way as any other number when submitted for approval.
The one significant caveat is the person's background. If the person wanting to be on the call list has a prior felony conviction, that does require an additional step. Felons are not automatically disqualified, but they do need to obtain permission from the warden before being added. That involves a formal request and a review process rather than a standard approval. It is not impossible, but it requires more effort than a standard submission.
Trusty camps operate with more relaxed conditions than higher security facilities, but the call list approval process works the same way. The inmate submits the number, the facility reviews the person associated with it, and approval or denial comes back from there.
If you are trying to get on the list and have a clean record, the prepaid phone is not an obstacle. Submit the number through whatever process the facility uses and it should move through the standard approval timeline without issue.