I have all my font sizes defined in pixels, e.g.
As far as I know, 508 does not specifically require that font size be adjustable, but experts expressly recommend allowing font resize. Nielson says:
Let Users Control Font Size: Tiny text tyrannizes users by dramatically reducing task throughput. IE4 had a great UI that let users easily change font sizes; let's get this design back in the next generation of browsers.
On this line, Section 508 § 1194.21(g) does state:
Applications shall not override user selected contrast and color selections and other individual display attributes
which includes font size and is compatible with the WCAG text resize success criterion that:
The author's responsibility is to create Web content that does not prevent the user agent from scaling the content effectively
So long as you're not forbidding text resizing (like using images of text or using the
text-resize-adjust CSS), you're good. But, at the end of the day, the use of relative font size provides for a better experience resizing text, which includes not just size of the font but attributes like line wrapping.
For these reasons, I'd consider relative font sizes important for aesthetics but not important for accessibility.