I use Wirecast to stream live to YouTube all the time.
I run it on my Windows 7 laptop connected to my Tascam US1641, but it only sees the inputs that Windows sees, so only Mic 1 and 2. It also uses most of the 2.3G Dual Core even to stream 240p. Between those two things it means that I run all the audio and mix on my studio machine and run line level audio via TRS>XLR from one interface to another.
There are probably ways to patch the output of Reaper to the input of Witecast, and my studio machine 3.6G dual core) might do the whole thing, but it's XP... Either way, I think it's better to use two separate machines.
Edit - BTW, YouTube actually is the right place to stream your video. The other popular places will force your viewers to create an account (who the fuck has a ustream account?) and log in if the want to actually watch your stream. I find out that if you just let it sit there asking you to log in, you can still hear the stream, you just can't really see the video. On YouTube everybody can watch for free, and if you're a bastard like me, you can even monetize it with ads and make a couple pennies in the process.
But the big reason to stream directly to YouTube is like the OP said, it shows up on your existing YouTube channel and the video is automatically added as an uploaded video when the live stream is over. I could not find a good way to get a video from ustream to YouTube. IDK if their paid service makes it possible, but on YouTube it's just free and just works.