Admin says that the order of tags does not matter at this time, so I think the first 3 should not be more important than the rest. However, the first 3 words of the title ARE the most important.
Google has been using only titles for search for a while now including on Etsy, so I would say that is true that Google doesn't use Etsy tags. The description would not be used for search either, but does show up under the title in search. It's mainly used to draw people to click once they find your item.
Drag and drop or a click on our most-used tags sounds good!