Taking a delayed screenshot in gnome-screenshot is only possible for a full screen capture.
IF there is a need to automate the process, the command line screengrabber scrot can do this. It only outputs to a file, but in good linux tradition, you can subsequently use another tool, xclip, to place it on the clipboard.
scrot -s -d 4 -o image.png
xclip -sel c -t image/png -i image.png
This will allow you to make a selection (s) and after a delay of 4 seconds (-d 4) write out to image.png, overwriting -o the file if already present. The second command will link the file to the clipboard (-sel c) as a MIME type image/png.
This could be wrapped in a script:
#!/bin/bash
TEMP=mktemp
scrot -s -d $1 -o $TEMP
xclip -sel c -t image/png -i $TEMP
mktemp creates a file with a random name in the /tmp folder. That folder is automatically cleaned on the next reboot. $1 is the first argument to provide to the script. So if you call the script for example ss, then the command ss 4 would introduce a delay of 4 seconds.