Yes, he clearly would, as this interview at the Christian Post makes clear:
Should a pastor continue in ministry if one of his sons, arriving at a mature age, proves to be an unbeliever?
Well, as you know, that hits close to home. So maybe the best thing I can do is tell you the way the elders at Bethlehem managed this, because that’s me.
When that happened, I went to the elders and I said to them, “Here’s the situation. I think my son needs to be pursued by the elders as far as you can, and then he needs to be excommunicated if he doesn’t respond.” He was 19 years old.
I don’t know what’s more shocking, that Piper was ready to excommunicate his 19-year-old son, or that his son’s sin was that he was (is?) an “unbeliever.”
What’s happened to Piper is that he got caught up in his own biblical hermeneutic. The Bible says this:
I left you behind in Crete for this reason, that you should put in order what remained to be done, and should appoint elders in every town, as I directed you: someone who is blameless, married only once, whose children are believers, not accused of debauchery and not rebellious.
What’s an inerrantist pastor to do when one of his children turns out not to be a believer? Well, step down immediately, of course. Right? I’m sure that’s exactly what Piper said and did. Let’s go to the tape: