Likely should inspect; whether you need to or not will depend on the municipality.
If your contractors are comfortable tackling the job on their own, let them. If they're uncertain and want the inspection, its probably worth having the inspection done.
Since January in Edmonton, Asbestos inspections are required on house demolitions (for infill etc.). I dont think they are required for interior basement demolition, but if you're feeling uncertain and suspect asbestos, its probably worth having the inspection & abatement done before you start the renovations.