Frank, does this mean you put your packages, stylesheets and palettes in Workbench?
I do not understand? I create/maintain my packages in Workbench, which is basically a different front-end of WL (please correct me if I am wrong). Stylesheets and palettes are only relevant in the Mathematica front-end as you can style cells (and elements within them) which are absent in Workbench.
It must mean that you do all of your development within Workbench and use straight Mathematica only with the deployed result.
No, from workbench you can 'run' your code, which pushes the code directly to the Mathematica kernel, pretty much the same as using Shift+Enter in Mathematica.
What happens if while using the application in regular Mathematica you find you want to update a routine, or stylesheet or palette?
Stylesheets and palettes are only used in the notebook enviroment from Mathematica. If I want to update a routine, i simply switch to Workbench, update the routine, hit the run button and test the function in mathematica (Or with an unit test directly in Workbench).
This means that you either have to go up to Workbench to make the change, and rebuild all the documentation [...] take care to keep them in sync.
This is thus not necessary, as you can run your code directly from workbench without building it first. I think you have overlooked some of the features of Workbench. I definitely recommend looking into these if you develop packages.