We can work with most anything your web designer can throw at us. Our process is to wait until the new site is live—we find that this prevents most need to re-work pages, which ends up costing you extra money.
What you'll do is give us a minimum 5 business day warning of the 'Go Live' day — send it via support request.
At that time, we will block out some time on the calendar of the person who will be building the template for you. If you lock in an absolute 'Go Live' day any earlier, let us know earlier.
When you actually flip the switch to turn on the new site, send us a support request and we will get our person started working on the new template. It's a bit harder than just subbing one file for another but we generally can get you a new template within several hours of the site going live.
Typically, what clients do is turn on the site, let us know so we can get our work done and when we're done THEN make the public announcement of the new site. The number of people who see the site when the pages don't match is pretty small so generally not a problem. We could, in the interim between when it goes live and when your site is done, build a very simple template that would have your new banner—then people won't see your old site on our pages and your new site elsewhere.