Short answer: no, he shouldn't need ftp access
Long answer:
If the person actually knows what they are doing, Wordpress in made in such a way, that it should only be needed to supply a proper module or template, that will then be integrated into Wordpress and then be a selectable in the menu, it's one of the great/easy of use things about Wordpress.
HOWEVER, more advanced functionality might require doing some alterations to the core of Wordpress or the like. Though in this case it just sounds like he needs to make simple CSS and html. In this case as a Wordpress developer/designer he should know how to make templates/modules and shouldn't require ftp access.
Some people might argue that development and testing is easier directly on the system, however testing and development should NEVER be done on a live system.