The 1/2" HC will prevent smaller predators from entering the coop/run. Just be sure that there are no other cracks or holes that are larger than 1/2"...around doors, roof eaves, windows, run corners, etc.,. As I said, dogs and large coons will go through the hardware cloth as it is no where...
A dog or big coon will go through the 1/2" HC....2x4 welded or woven wire would come closer to stopping them. A 2-3 foot piece of 1/2" HC attached at the bottom of the 2x4 fencing would keep coons from reaching through.
Ahavati, being in deep south Texas I would think your concern will be...