Nope.
There is an FAQ that in essence says if you somehow have an ability to make multiple attacks on a charge, that only the first attack benefits.
The FAQ was originally written around the interaction between lance and spirited charge, but I think it's pretty straight forward to extend it's application.
In essence, the iterative attacks require you to swing again and again, and so don't benefit from the momentum of the charge.
Lance: If I have the pounce ability and I charge with a lance, do my iterative lance attacks get the lance's extra damage multiplier from charging?
No, it doesn’t makes sense that those iterative attacks gain the damage bonus. To make that second attack, you have to pull the lance back and stab forward again, and that stab doesn’t have the benefit of the charge’s momentum. (The Core Rulebook doesn’t state that you only get the damage multiplier on the first attack with a lance because when the Core Rulebook was published, there was no way for a PC to charge and get multiple attacks with a weapon in the same round, so that combination didn’t need to be addressed.)
No need to extrapolate anything.
This FAQ says "During a mounted charge, you deal double damage with your first melee attack made with a lance or with any weapon if you have Spirited Charge (or a similar effect)" Emphazis mine.
The way it's written, it wasn't accounting really for the ability to make multiple attacks on a charge and so people overlooked the wording of "first" because it didn't really seem like it applied.
But between both FAQs, it should be pretty clear.