Does iMac use the Internet while in Sleep Mode?

To be completely accurate the Mac will wake periodically to perform various tasks, some of which will want Internet access. Checking for updates will use the Internet to cite one trivial example, and it's not in Sleep Mode while it does that. It's something Apple calls "dark wake" and its functions depend on the exact model iMac and the operating system it's using.

Read more: What is Power Nap on Mac? - Apple Support

What exactly do you mean "Is iMac using the internet while in Sleep Mode?" That has ZERO context, if you are asking does it surf to web pages while asleep, nope it does not. If you mean something else please state that!