Any image assets listed in the Insert Image screen can be searched. But that search apparently does not include tags. You have to go to the Asset listing page to filter by tag. Idea: On the Edit Asset page, provide a File options screen (the same that is loaded after the user has picked an image in the Insert Image screen) to generate the code to then insert into a new Entry. At present, there is an Embed Asset link, but it merely allows you to copy the asset path.
Reported on Movable Type 4.2
Obviously it would be convenient if you could filter by tag in the Insert Image screen - also with regard to custom fields for assets, which load the same screen to pick an asset.