ladies and gents let's discuss
It shows you respect yourself & your wife.
I cann't imagine any of my in-law coming to stay in my house without my knowledge or my family member coming to stay without my husband knowledge!
Unless your house is a family bus-stop where different people drop by without notice? Then you should be prepare for the consequent like unmanageable finance, time management etc
Yes of course but that is not to say you are seeking her approval. Simple courtesy. Problem is that even if you forget women will always make a mountain out of it and funny enough if they are the one inviting, they care less believing you would most certainly approve especially if its their sister.