Lost database

I’m moving a website from one server to another and the helpdesk failed to inform me that I needed to copy the database. Therefore I have a copy of my entire site backup along with an xml export file on my mac.
The old site on the previous server has now been deleted by the hosting company although they do have a backup which they can access and forward on to me at a considerable cost.
Here’s my question. Would the following work?
I create a new wordpress site using the tools on Bluehost and then import the site using the xml file. I then add the content folders from my mac into the appropriate places.
Cheers
Jason