adding certificates to the app service plan will not trigger anything, however chaing the binding to you web app could result in a new IP, but you can choose static on the web app.

But unless you are using a root domain name like mydomain.com, then i would suggest you not use static ip and use CNAME instead, as long as its a sub domain like myapp.mydomain.com then you can use CNAME. Remeber to keep the DNS TTL low when using cname.