I've been debating this to myself for the last few minutes, and I'm seeing reasons for both yes and no. This stemmed from looking at the answers to Java HashMap vs. Hashtable and seeing several people say Hashtable is in fact slower.
It seems to me that a synchronized method should act absolutely no different than its unsynchronized counterpart if running in a single thread, since the action of synchronizing shouldn't block anything. That said, I would imagine the compiler handles the two cases differently and that's why people are saying synchronized is slower.
Not that it's by any means conclusive, but I ran some simple tests on HashMap vs Hashtable, and saw little difference in speed.