Sure in general you need drivers for a device to use it on Linux. This question is more about a class of programs in which you could say the program itself is the 'driver'. A lot of apps use usb in a way like you used the good old rs232 port ('COM port'). That's the type of USB which will be supported in Wine at some point and perhaps some very basic normal usb drivers like ones for reading keys from dongles (copy protection).
So what won't work is installing the HP drivers for your new all-in-one printer for that you need a native driver.
