Am I right, can this app be used as a replacement for the standard white remote when streaming content?
The answer is almost, but not completely. You can use the remote app to browse your

TV library (and it shouldn't differentiate between synced or streamed content), select and play (and stop, pause, etc) any of your movies, TV shows, music, music videos, podcasts, etc. For music you can control volume, and specify which speakers (via airtunes) play the output.
What you
can't do is navigate the rest of the

TV's menu. You can't access photos, settings, or YouTube (but read on), nor can you select the on-line portions of the Movies and TV Shows menus (via the ITMS), like movie trailers, rentals, or TV shows for sale.
The kind of screwy thing is that you
can use the Remote app for any searches that require text entry, like for movies and TV shows on the ITMS, or YouTube. When you navigate to a search screen (using the white remote) and you have the Remote app running, a search screen pops up on your Touch (or iPhone) where you can type in the text, rather than using the white remote and the onscreen text selection. This turns out to be a much easier way to enter the text, but you have to have two devices on hand to do it.
Regarding synced and streamed content, I have a 40Gb

TV and way more content than that in my library. I don't configure my

TV not to sync; I just let it sync what it wants and stream the rest, by default. When I use the Remote app it's just like using the white remote -- there's no distinction in the library listings, synced and streamed both look the same and work equally well.
Hope that helps.