You may find that you need to redownload the store content again. But if the previously downloaded content works (try just a small number of items first and test), then of course that's more convenient. When I switched from an Origin install over to Steam entirely, not just by using Steam codes, I had to redownload everything from Store Account history because nothing worked -- though that's a very different scenario than a new base game registration having been applied.
Yes, you can just dump DCCache and DCBackup if you are starting to build the content up again from scratch. Note that DCCache also contains your sims3pack CC content, so those will need to be reinstalled as well if you go that route. The ebc files are store content, the dbc files are custom.
