Definately, although google will find the new page/s, I’m a stickler for crossing the T’s and dotting the i’s, so I always do a fresh xml in this case.
I use the following software it’s free –
xxxhttp://devintelligence.com/SitemapGenerator/
Especially good when your site is dynamic, it grabs all pages 
It’s also great as you can edit out pages from the xml.
Cheers