While I speak heresy in the face of VOGONS by saying SATA on a 3.11 machine is pointless, I unfortunately have to stand by it.
Interesting? Yes.
At all a good idea? Noooooo + o^24642
Not only will you be wasting almost every single GB of storage on that hard drive, you would get compatibility issues not just with Windows. There is one option though. Find a SATA controller that supports legacy IDE emulation mode. This basically makes the SATA controller look like IDE. It's available on slightly newer systems however, and for an old PC with an expansion card will have to be an on card BIOS setting. This should however solve any issues, removing the need for drivers.
That makes it possible, and it will work, but the issue arises when you realize that no matter what the file system, Windows 3.11 can not access more than 2GB per partition (Possibly per drive, have not checked). So you're either gonna have to make LOADS of 2GB DOS partitions on something FreeDOS or Dos 7.1 (euugh) or deal with most of your drive being unusable.
There's also the speed. Due to IDE legacy mode, you will be limited to at best 133mbit/s and at worst less. Aside from maybe an access time increase on the newer drives (Which can be had with flash storage anyways) you won't get any benefits.
But as I have previously said, Welcome to VOGONS! Do your crazy shit NOBODY in their right mind would. I am using a 2004 IBM EServer as a regular, every day server, and a Athlon 64 x2 as a HTPC. I still print using Dot Matrix too.