As long as it is safe, I don't see anything that prohibits thrusting with an axe. It just says that blunt can't be used to thrust and that if you intend to thrust, you have to have a thrusting tip.
"Blunt weapons, axes, one handed spears and polearms must have a padded head that is shaped appropriate to the weapon type. This padded head must be made out of foam and it must be placed over the 5/8” pipe insulation that covers the core. The head must be noticeably thicker than the pipe insulation and should squash easily. Everything above the grip area must be padded – like all weapons, any part that might come into contact with your opponents should have foam padding. Note that blunt weapons may never be used to thrust."
Again, I could be wrong as well. The weapon construction guidelines leave a lot open to interpretation by our local rules/weapons marshals.