YES, you should apply to DYS for your 8yo, if the offerings sound like they may be of interest in the near term or throughout the next decade (children age out at 18).
With a score at the cutoff on an approved test instrument (https://www.davidsongifted.org/gifted-programs/young-scholars/admissions/eligibility-and-testing/
), I encourage you to apply to Davidson Young Scholars (DYS). It cannot hurt to apply, and over the years your child, you as the parent, and ultimately the whole family may benefit from the knowledge, insight, support, and potential camaraderie you may have opportunities to engage in with other DYS and DYS families.
You probably saw the DYS application process online, and I will link it here, for convenience of yourself and also future readers of this post who may wonder what DYS is, and how to apply. https://www.davidsongifted.org/gifted-programs/young-scholars/
There are many related webpages... follow the links... be sure to click on each one to get all the detail available.