Generally speaking - no, Wine cannot run drivers for you. Wine is an implementation of the Win32 API on Linux, just as Windows has that implementation built-in nowadays. Remember "Wine is not an emulator".
There are however projects to use Windows drivers with Linux - for WLAN there is the
ndiswrapper project. This may seem really helpful, but in the long run it is counter-productive. Using binary Windows drivers as second rate Linux drivers using a wrapper is no long term solution and to make matters worse, WLAN vendors are already starting to claim their hardware "works in Linux" just because of this. A better solution would be users and developers teaming up against hardware vendors, requesting documentation for their products since in the long run this makes both vendors and users happier. Sales is good for hardware vendors, usable drivers are good for users.
Wine has been reported to implement the win32 API and other API's so well that with the right DLL's loaded you can indeed infect your Wine installation (i.e. the ~/.wine directory in your homedir). This is of course not much of a dangerous issue since one should never run Wine as root - there is no reason to do it. I also have a hard time thinking anyone would actually create a Windows virus which would inflict system wide damage on a Linux installation when executed in Wine...at least not in real-world circumstances (a.k.a. "the wild"). From the virus creators' point of view there are simply too many Windows users to harass with virii and the chance of anyone running Wine is minimal.
Håkan