Stop State Toggles background processes?

If you hit Stop ICON or use the Stop (All) block:
Any background code will operate/stop operating.
I use a condition based on time. The background will execute sometimes when a STOP is hit. But if STOP is executed, It will not execute that background.

It also happens to "Key" based processes.

I'm not entirely sure what you're talking about. When key pressed hat block run whenever you press that key, even after you hit the stop button. This also goes with any other hat block event. The only one that stops when you hit the stop button is the generic when block.

since [scratchblocks]
when <> :: control hat
[/scratchblocks] ?

Since the block has existed (I think). The stop button turns into a square when there's a when block, which shows that the when blocks don't run. If you click it again, they start running again.