Does "clear data" of a running app also "force stop"? In settings, if you go to an app and click "clear data" does that also cause the "force stop" function to be activated?

I'm thinking that when you clear the data of an app, the app is basically returned to the state it was in when you just installed it, so it necessitates a "force stop". Is this correct?
Yes, you are correct.  Any running app will be stopped if you clear its data, which you can verify pretty easily by selecting an app from the Running list in Settings &rarr; Apps and clearing its data; it will disappear from the list.  I verified this myself quite a while ago out of curiosity.  It is, of course, expected for the reason you mention &mdash; getting rid of the data that the app was working with will almost certainly make its state invalid or could cause partial (i.e., corrupt) data to be saved later.