I never change URLs, especially if the URL gets traffic. If you want to target a new keyword you should start a new page shouldn't you?
That said yes WordPress will automatically create an SE friendly redirect but it's not 100% reliable. You don't need to update the test link in the post because Google will do that for you (eventually) but if you have a bunch of redirects the update process isn't as reliable.
With all these uncertainties I'd def recommend you create a new page
