Yes, they run slower. From Tom's Hardware, December 2008:
Gearlog was benchmarking to test third party RAM modules for use in the new MacBook Pros, but discovered that the notebook’s processing power significantly decreased after the battery was removed during the test.
Gearlog’s own results show a decrease of 36 percent in processor speeds without a battery attached on their unibody MacBook Pro. Our own tests show a decrease of 50 percent when rendering with one CPU, a decrease of 52 percent in multiprocessor rendering, while the GPU suffered a 40 percent decrease in performance.
Apple used to document this in HT2332 (but the official link is dead):
MacBook and MacBook Pro: Mac reduces processor speed when battery is removed while operating from an A/C adaptor
If the battery is removed from a MacBook or MacBook Pro, the computer will automatically reduce the processor speed. This prevents the computer from shutting down if it demands more power than the A/C adaptor alone can provide.
Important: It is strongly recommended that you do not use your MacBook or MacBook Pro while the battery is removed. Accidently bumping the A/C adaptor could disconnect power and shutdown the computer. Any information that was not saved on your computer would be lost.