Would it?

As long as you don't run wine as root, how should it? But even then I doubt it, in my opininion even if it is able to infect an other program, lets say ls, it wouldn't really run, because it depends on functions of the Windows environment. But it is not running anymore in the wine environment when started by a native program.

If u execute the virus .exe or the autorun file of that .exe if the virus is about starting and running a process then it starts it and you can see the running file in system processes monitor but it does no harm as it is not windows (like disabling task manager) even though you delete the process it comes again as it is written to execute as long as the autorun file is present in that drive

If its code is about creating a newfolder inside every folder then it is difficult as it requires some command line jobs which differ by environment.

But In my view as long as it limits only till exectuing a .exe file or doing some simple process starting it will run in linux environment also with the help of wine .But it also requires some little effort from your side to make it run the first time