Does tea play a significant role in kombucha fermentation?
You do not have to use tea to make kombucha. For example, the Noma Guide to Fermentation contains seven kombucha recipes, none of which use actual tea. A recommended way of storing SCOBYs when not brewing is to store them in a water + sugar solution, which needs to be refreshed every so often. Thus, your suggested method of making "kombucha" from water + sugar, then mixing with a strong tea would work in principle. 

That said, I would expect the result of this method to be essentially a mix of tea and acetic acid, with little to no added complexity of flavour. For me, that complexity is most of the fun of making kombucha.