Possibly, but it's time consuming and quite difficult, You would need access to a good microscope, and you could then look at the lateral wall of the beak, it will show growth rings rather like a tree, possibly of daily periodicity. However, I don't know if this has been attempted for a GPO, their beaks may be too heavy and dark to see through!
Wouldn't mind giving it a go, but GPOs are scarce in NZ. Here's a (not very good) pic of the lateral wall of one of our small species (way way way smaller than a GPO, ~20cm total length!!!)
If you all are wanting to try it out, I will keep an eye out for a deceased GPO when out collecting and talk to the fishermen and see what they are pulling in. Most of the octos that make it ashore with the fishermen are dead anyways and all they want are the tentacles not the mantle.
I currently have 4 GPO beaks in my possession with weights maturity and sizes. I'm going to attempt to give it a go so will let you all know how I get on. I'm not sure if they will do daily increments as their water is very cold.
Well, Kerry, we're not so warm here and it works!!!!! BUT what concerns me about GPO is the size, the beaks are likely to be very dark and hard to see through, you may need to mount them and section much as it done with some of the large onychoteuthid gladii.