Can my Home Owners' ociation enter my home without my consent?

If they own any part of the condo or have to provide insurance for it, any wall, the roof, balcony, plumbing, etc, they have every right to inspect it, and may actually have to for insurance doentation. They will not need your consent if they own any part, they just need to give you notice, which they have done. They will not be breaking in at all, not if you are illegally preventing access to their property.