You can experiment with this AHK script. I'm using AutoHotKey_L
as sometimes that makes a difference.
For it to show the ToolTip you need to have the left mouse button down, then press and release the Left Control key. If you prefer right control key change LControl to RControl.
Should work for situations where you can select with the mouse, then keep the
mouse button down. The ToolTip clears the next time you click the mouse.
The reason for that is if it's active regardless of the mouse button state, it will be churning stuff to the clipboard to get the count. Also it would likely interfere with using the clipboard normally. As it is, in the script I save clipboard text and restore it. Saving everything, such as large graphics, would likely slow it down quite a bit.
If you get it to work to your liking you can compile with AHK_L and even add a custom icon to show in the tray. To get it to display the icon compiled into the exe, use these lines near the top:
Selected Count Script
count := 0
Selected := ""
SaveClipboard := ""
if not GetKeyState("LButton")
SaveClipboard := Clipboard
Selected = %Clipboard%
if not Selected
Clipboard := SaveClipboard
Loop, parse, clipboard, `n, `r
count := A_Index