Is there any way to check what the current status of hntpos-bsy button is for a given station?
I'd like to use AES SMS for this if possible.

For a H.323 or DCP station you can use the DMCC APIs to check/monitor button state (lamp state). If only FACs are being used to activate/deactivate the state then you won't be able to observe the state.

https://www.devconnectprogram.com/site/global/products_resources/avaya_aura_application_enablement_services/releases/8_01/index.gsp#tabs-product-downld-7

The System Management Service Web Service only accesses information taht is available through the System Access Terminal (SAT), and that is largely provisioned information and not status information. You could check the status station form, but I don't recall hunt group position busy status information being shown, but all of my systems are setup for EAS, and the button does not apply in that configuration.