Will asynchronous change in a context variable with flow-scope, be immediately noticed by other nodes in the flow?

In short, No. You must query the global/flow variable to get its current value, and then act or process that value accordingly. Check out the following for details...
https://nodered.org/docs/user-guide/context

And this is also a interesting read...

You could setup a flow to poll the value, and then take action on change of value. Others in this forum may have setup something that is a bit more elegant, but as I said, there is per my understanding no trigger on value change logic.

I believe this topic has been discussed at length in the following thread...