Would it be possible to have Steam run linux ready games natively, and non-linux based games through wine without having to run two instances of Steam?
Even if it could be technically possible, you can't be logged on the same Steam account at the same time in two different clients, and I imagine that you wouldn't have two accounts with games split around.
Running games on wine would also be game-dependant more than steam-dependant since each game has it's own requirements and prerequisites, therefore some might work, some might not. A better solution would be running dual boot, or a virtual machine, with both linux and windows, but I wouldn't rely on a virtual machine's performance.
Now is posible to connect two clients (Linux-native and Wined-steam) in same machine in same os.
The dual login is now possible because of Steam Home Streaming feature, the restriction login changes and life goes easier for us.
*NOTE: IDK if Mac users can use this feature, but Linux user can use Home Streaming, i use it daily the webpage is outdated (10/22/2014).