It does often have that surface-level message: Good people will always prevail, evil is a necessary part of the status quo, etc. But that's always part of the joke.
I don't think anyone leaves South Park episodes thinking "wow that is so true" and having introspective thoughts about our country. It's more like "what the fuck did I just watch" and "that's about right," dismissive of the average American lifestyle or unhappy with the problems we often face.
I'll keep that in mind though. Interesting perspective.
Sure on one hand that's the joke, but I feel they never really subvert or question that joke (again with the caveat I really haven't seen much from the last ~10 seasons or so). As long as our heroes stay true to their Real American Values nothing bad can ever happen to them. Now I could be wrong, but the way that that message permeates everything the creators make feels genuine.
Watching from outside the US it does feel pretty solidly pro US. The core message seems to be that sure, we have some dumb politicians and occasionally our huge companies do some dumb and evil shit, but that is the aberration. The Real America is made up of fundamentally Good People striving to do the Right Thing and that will always prevail over any temporary glitches in the system. All the criticisms they levy are the same criticisms being made at the time by all Good Americans.
The show is obviously made by two people who love their country despite/because of all its flaws and that clearly shines through.