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:
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:
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:
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.
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.