Can the terms of a temporary care and custody agreement include specific parenting time for the other parent?

Yes, in practice a temporary care and custody agreement can, and often does, address contact between the child and each parent, including the parent the child wasn't living with when the agreement was made - though the CYFSA's own term for this kind of contact time is access, not parenting time. The agreement can set out how much access each parent has, how visits are supervised or arranged, and what conditions apply, since the society still has an interest in maintaining the child's relationships with both parents where it's safe to do so.

This access under the agreement is separate from, and doesn't automatically replace, any existing family court parenting time order between the parents themselves - the two can end up overlapping or, in some cases, not quite matching. If you're the parent the child wasn't living with, don't assume the society will automatically build in access that reflects your existing family court order; ask specifically that the agreement address your access, and get legal advice about how the agreement's terms interact with your existing parenting order so the two arrangements don't work against each other.