Unless the there is a dual-core patch or dual-core support for the game you want to play no.
For example ...
Athlon 64 3200+ - $150
512k L2 cache
2.0ghz
Athlon 64 x2 3800+ - $300
512k(x2) L2 cache
2.0ghz
The Athlon 64 x2 3800+ would perform exactly the same as the Athlon 64 3200+ because since only one core of the dual-core 3800+ can be utilized, it's just as powerful as the single core 3200+. Remember, even the 2x512k that is doubled on the dual-core model can only be used as 512k because each core strictly has 512k of L2 cache.
However, more and more games are beginning to take advantage of dual-core, so it's a good idea to do dual-core if possible.
Remember, this only applies to non dual-core supported games, dual-core supporting or patched games will crush single-core processors.
If you like to run other applications and multi-task during gaming though, the dual-cores will run significantly faster than the single core, because one of the cores can be devoted to gaming while the other can be used for any other applications you are running at the same time.