Sure, the fouls are penalized. No reason not to.
Many people think that a false foul is this thing that you have to rule on and call correctly and this and that. A false foul is no big deal. But it's not. In fact, it's just a term to describe the situation. It's simply when a foul occurs, followed by another foul before the clock restarts. It's really not an issue. Just penalize the fouls in the order in which they occur.