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.
Asbestos can be quite hazardous to your health and is well documented. It’s friable which means it beaks easily into very small pieces when disturbed. Especially if cut with a saw, for example. It’s also the same weight as air, so once released it drifts around in the air for a very long time, where it can be inhaled into your lungs and will stay there forever. Hence the lung hazard.
It costs a few hundred dollars to have the material tested. We tested on two older houses before Reno’s and the asbestos was in the bottom layer of the kitchen Lino. Small amounts of asbestos were present so we put on a mask and broke up large pieces with no power tools, and hauled them outside. We also placed a couple of fans pointed towards open windows to blow out any asbestos. Risky? Probably.