In my opinion, multiple roles are possible. TEA can be a complexing agent for metals such as Cu or Ti... For other metals, it's possible that it's chelating behaviour is too weak to really consider it as an complexing agent. So it depends which metals you are planning to use...

Nevertheless, it can be quite useful in a chemical solution due to it's high boiling point (around 320°C), allowing a greater 'flexibility' to your coating at lower temperatures during processing.