First of all, there is (on Windows) a special user “Downloads” folder interface that can be changed to point at any folder. (Open explorer, navigate to your user home folder. Right click the “Downloads” icon, and choose “Properties” from the context-menu. Switch to the “Location” tab. Change the path to some other folder if you wish.)
Most browsers start out using this as their default downloads path after installation, when first run by any particular user account. But can be changed later, …
For extra-SketchUp downloading, this is set in the particular browser’s settings. (And affects all websites, not just EW or SketchUcation.) But you can set a different download folder for Chrome and MSIE, if you desire.
These per browser application settings do not affect the user setting for the special “Downloads” folder path (1st paragraph above.)
From inside SketchUp, the Extension Warehouse uses it’s own local Storage or the TEMP folder, and cleans up later it appears. (Ie, the installed RBZ does not go into the “Downloads” folder set by MSIE settings.)
For the SketchUcation PluginStore, a request would need to be made to TIG.