You might try asking in the parents forum. But I can’t see how a very heavy courseload and having time for your page duties would mesh well together. That said, I’d encourage my own kid to take the page opportunity for sure. HS academics are just play compared to college anyway – make sure you get they some kind of honors or AP Calc for sure before graduating, take some kind of bio/Chem/physics, and (literally) everything else can be made up. The page program would be a legit explanation for fewer APs, too.
Colleges like students who do stuff that is different than their peers. The page program would be far more interesting to them than 5-6 more AP classes.