steamsteam-family-sharing
Yes, playing a non-sharable game locks me out from Family Sharing. However, does playing a third-party game which only has an icon in Steam lock me out from family sharing? I have to register it because I have to play it with a Steam Controller.
The answer linked earlier seems to say otherwise, but I need a clear answer.
When this question was asked, Steam Family Sharing was in beta. However, as of March 3rd 2014, Steam Family Sharing is out of beta and available to everyone.
If you open that tab now, you should see a screen like this:
As Scott Weldon said, there doesn't seem to be any way to do this other than disabling sharing of the friend whose library is in use, or using offline mode as Jaxir said to prevent the library from being in use in the first place. You can change the order in which your friends share libraries with you by having them unshare and reshare the library with you, in order to play your games with the library of whichever friend is least likely to be using it, but for a general solution to choose which friend's library to use, you'll need sfs-select.
SFS-select is a python tool to enable and disable friends' shared libraries by modifying the local cache remembering which accounts have authorized you. It's a bit of a clunky workaround, but it lets you pick exactly which friend's library you would like to use for a shared game, without needing your friends to log in to your computer again, or changing the actual permissions registered on the Steam server at all. It includes both graphical and command-line versions. You can download it here or read about it on the Steam forum thread.
Best Answer
From my experience, it doesn't: I also have Overwatch and other Blizzard games on my main Steam account, while I have Dark Souls III shared with a second account (In order to fix the covenant bug). Since Steam counts Blizzard Games as being "played" while the Battle.net client is open, and I've played Dark Souls III during that time, I would assume there are no limitations.
This is probably due to the fact that Steam only creates a shortcut to launch the game, instead of having an steamapp entry for it (Like you would have a shortcut on your desktop).