1. If we were to leave the English phrase in, would that in any way hurt?
Hurt? Not particularly. I've done it both ways and haven't noticed any significant impact one way or another. The URL beyond the domain name doesn't seem to hold as much interest for the user in Asia.
2. Is there any evidence that translating the phrase into the local language has any effect?
Look at DMOZ. They went all the way not just translating, but actually encoding the entire URL (after the domain) into the local language. That may work well for highly structured directory or wiki sites, but the trend certainly hasn't carried over to the mainstream Japanese and Chinese sites I monitor.
The most popular SE/Directory in Japan, Yahoo Japan, uses English in its URL structure for the directory.