First of all: the Pipe does not need to be public to be able to add it to Google Reader. I have dozens of Pipes and I have not published any of them.
On the other hand, I also think there is a problem. When I generate a new Pipe, I cannot immediately add the output to Google Reader. It takes some hours before I am able to add it. I don't know the reason but what I do is the following: I copy the RSS address of the Pipe output to somewhere and try adding that same address a few hours later. The I start seeing the output in Google Reader (and yes, it also detects the name of the Pipe, so you don't have to rename it again).