Perhaps a bit, but 64-bit allows you to use more RAM, whereas 32-bit max's out at 4GB. Adding more RAM will definitely affect your gaming, for the better.
My Computer
At a glance
7 Ultimate x64/7 Home Premium x64Intel i3 550 3.2 GHzCorsair 16 GB DDR3 (4 X 4GB)Intel HD Graphics
Computer Manufacturer/Model Number
Dell Inspiron 580
OS
7 Ultimate x64/7 Home Premium x64
CPU
Intel i3 550 3.2 GHz
Motherboard
Dell/Intel H57
Memory
Corsair 16 GB DDR3 (4 X 4GB)
Graphics Card(s)
Intel HD Graphics
Sound Card
Intel P55 HD Audio
Monitor(s) Displays
LG E2360 LED
Screen Resolution
1920 X 1080
Hard Drives
Seagate 1TB X 2 Internal,
Seagate 1TB eSATA (Backup)
PSU
Dell 300W
Case
Dell Inspiron
Cooling
Dell/Intel
Keyboard
Microsoft Wireless Comfort Keyboard 5000
Mouse
Microsoft Wireless Mouse 5000
Internet Speed
4,000 Mbit DSL
Other Info
Custom Installation -
OS separate on C:
Pagefile Separate on P:
Program Files Separate on U:
Users and ProgramData separate on V:
From my observations with a 32-bit XP installation and 64-bit Vista and 7; the newer versions take up roughly double the memory for 64-bit versions (but again, this was compared to 32-bit XP).
As bbearren says, 64-bit machines are able to take more memory, which helps not only just to run the OS itself, but in some newer games such as Skyrim.
My Computer
At a glance
Windows 7 Ultimate 64-bitAMD Phenom II X4 955 Black OC'ed 4.0GHz8GB Mushkin Enhanced Silverline (2x4GB) 1333XFX Radeon HD6870 1024MB GDDR5 OC'ed 945MHz; ...
There are several benefits of going to Windows 7 64-bit:
With 32-bit Windows, you can use a maximum of 4GB RAM. 64-bit Windows 7 runs very fast with 4GB and you can upgrade your RAM to 8 or 16 GB later, making your system future-proof.
A 32-bit OS can theoretically use up to 4 GB of RAM, but 32-bit versions of Windows Vista and Windows 7 see a maximum of 3.12 GB. With 64-bit Windows 7, you can use the full 4GB RAM.