I'm vaguely involved w/ ShareX, so take this however you want.
It doesn't as of a recent update (due to continued stability issues at Imgur). The default behavior is to not upload anymore.
Additionally ShareX pops up a big red warning telling you that you're about to upload. There are some forks (see: ShareNot) that explicitly remove any uploading, but by default there is a registry key, a setting, and a big warning that you can enable that disables uploading.
https://www.xbox.com/en-US/gaming-copilot