Aaaaaaaaaaaaaaaaaaaaah, Gee I feel like an idiot!

I actually thought that elbow was actually still fitted properly, and that the hole was an extra spout.
I also know what might have caused it to break, as I have been yanking at that hose multiple times while installing the plastic cover of the right headlight back after several low-beam adjustments.
Thanks a million guys.
One question though: the broken off part seems to be still attached on the inside of the opening. I guess I can push it through to fall inside the radiator, but the question is: There really isn't any problem in that part sitting inside the radiator while it's running for extended periods of time?
Sam