Our organisation is looking to upgrade to SAP HANA under an SAP ECC 6.0 EP7 environment. Would moving to a HANA backend change the SAP GUI API process at all? I understand that there is always the possibility that in the upgrade specific fields/columns may be renamed/changed, I'm more interested in understanding whether the process for using the API will be affected.
SAP ECC just like all SAP NetWeaver-based products employs a 3-tier architecture. A core aspect of this is that the presentation layer (SAP GUI) is completely decoupled from the data processing (Application Server and SAP HANA nowadays) and data storage layer (SAP HANA).
In short: you can upgrade/change/modify whatever you want on your SAP HANA and SAP GUI and your front-end won't change a bit.
From your question I get it that you assume that upgrading SAP HANA would affect the actual business programs of ECC (and thereby changing UI elements). This is not the case at all. If the ECC component get upgraded things like that might be part of the upgrade, but again, this doesn't change a bit about the UI, as the definition of the UI is part of the ECC component itself. SAP GUI is really just the rendering tool here. Think of it as the "Web-browser" for your SAP application, where the SAP Application server delivers the UI-description similar to a WEB-server that delivers HTML pages.
All this, of course, has nothing to do with SAP HANA ...