Is it possible to adjust sleep mode so that I can continue to share files while Windows 7 is set to sleep? If so, what settings should I use?
However as stated in the description, hardware support for this feature is generally limited to Media Center PCs:
Away Mode is a Windows feature that is designed for Media PC scenarios. Away Mode enables the Windows PC to appear off to the user, when the system is actually operational and processing background media tasks such as recording television content or streaming media to other devices.
If your PC supports Away Mode (you might still need to toggle related power settings in the BIOS), you'll see an additional Multimedia settings option when you change the advanced settings for any power plan:
Some recommended settings are listed in this article.
Even if you don't own a Media Center PC, you can try enabling Away Mode forcibly by editing the registry and changing power plan options as mentioned in this article (basically, create a DWORD called AwayModeEnabled with value 1 under:
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Session Manager\Power ).
The Microsoft document from the first link above has more details, including how you can use the powercfg command's Query Hidden Settings parameter to query Away Mode status:
powercfg /qh SCHEME_CURRENT SUB_SLEEP
as also how you can use powercfg to modify Away Mode settings related to AC/DC power and so on.
I've just added this information here because it's interesting and not widely known and you can certainly try it out if you want, but it's quite likely that for your hardware Mixxiphoid's answer holds true.
Sleep is a power-saving state that allows a computer to quickly resume full-power operation (typically within several seconds) when you want to start working again. Putting your computer into the sleep state is like pausing a DVD player—the computer immediately stops what it’s doing and is ready to start again when you want to resume working.
From the Microsoft site. Asking the computer to be used while in sleep mode is like asking the DVD player to play while on paused mode. So that won't work.
Short answer: It is not possible.