It's a client-side setting, but as with most things, there's a group of GPOs you can configure to control client offline files as well.
To simply check its status on a client, probably the easiest way is to open up the Sync Center
in the Control Panel and go to the 'Manage offline files` link (which you can also get to by typing "offline files") into the search bar in the start menu.
As to turning it of for specific folders, that's a Windows 8/Server 2012 GPO feature that I don't think is available for Windows 7. I'm pretty sure that for Windows 7 you'll need to do some scripting magic with the net share /cache
switch in a logon script or the like. It's very doable, just not as clean and easily manageable as as a GPO. This is what I use in our domain to set which shares users cache into their offline files stores, though in your case, I guess you're looking for /cache:none
.