can I configure media inserts to use relative paths?

I’ve noticed that whenever I insert a graphic into a page, regardless of theme, that absolute paths seem to be used in the SRC attribute of the generated <IMG> tags. This never mattered to me personally, but in the past I had been advised by my hosting company that they prefer pages to use relative paths whenever possible. Can wordpress be configured to prefer relative paths?

One of the reasons is because I often want to keep some of my graphics in protected directories. Protected directories usually allow access by pages already in the domain, but reject access when a direct http:// link to the graphic is used. There are other advantages too.