As you've figured out by the lack of response, I don't think any of us use HAI. I use an Elk M1G and can trigger things via the Elk's keypad buttons, but I had to modify 123's M1G module to allow binding a keypad (Home object) to the buttons on the keypad device object.
Since HAI is an add-in, you do not have this luxury as the source code is not exposed. I would read all the Premise help files on the HAI OmniPro, examine the relevant classes the device objects and see if any of the HAI Omni classes inherit from the keypad class. If they do, try binding a keypad object with them. If that doesn't work, extend the binding source property to the relevand HAI Omni class to allow binding.
If the above still doesn't work, you can still integrate the keypad buttons, either by:
1. creating a completely new HAI Omni class from scratch (last resort) OR
2. by having a second connection to the OmniPro controller (if this is allowed by the controller) and just building a stand alone Premise module with the sole purpose of communicating with the buttons