Only if the user has delved deep into their prefs. "Always use my fonts and sizes" (exact wording of course depends on browser) is never the default.
What, exactly, is so riveting about your body text (again: NOT headings) that it will lose its impact if read in, say, Palatino instead of Times, or Helvetica instead of Arial?
Express your font sizes as a percentage of the default, and everything will stay nicely in proportion. Use explicit numbers and the user will be forced to deploy the browser's "zoom text" menu option, creating a new sequence of sizes that may or may not still be in proportion to each other. Net result: irritated user and site that ends up looking even less like your original vision.